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SageMath
E = EllipticCurve("i1")
E.isogeny_class()
Elliptic curves in class 257070.i
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 257070.i1 | 257070i7 | \([1, 0, 1, -9807977879, 364283420931002]\) | \(104342717923500104934595071389480809/3055818618359193313321992000000\) | \(3055818618359193313321992000000\) | \([2]\) | \(780337152\) | \(4.6270\) | |
| 257070.i2 | 257070i4 | \([1, 0, 1, -9737976464, 369870965973686]\) | \(102124483650585555251925620404048249/2741948777894661145800\) | \(2741948777894661145800\) | \([6]\) | \(260112384\) | \(4.0777\) | |
| 257070.i3 | 257070i6 | \([1, 0, 1, -1447977879, -13157203068998]\) | \(335744953072408644363237149480809/119513838730245696000000000000\) | \(119513838730245696000000000000\) | \([2, 2]\) | \(390168576\) | \(4.2804\) | |
| 257070.i4 | 257070i3 | \([1, 0, 1, -1289380759, -17816596138054]\) | \(237064905531150935141805799085929/61758542254543208448000000\) | \(61758542254543208448000000\) | \([2]\) | \(195084288\) | \(3.9339\) | |
| 257070.i5 | 257070i2 | \([1, 0, 1, -608647464, 5778718527286]\) | \(24935676874284912650568916672249/4085384621399713728360000\) | \(4085384621399713728360000\) | \([2, 6]\) | \(130056192\) | \(3.7311\) | |
| 257070.i6 | 257070i5 | \([1, 0, 1, -549710784, 6942552934582]\) | \(-18370732847116261028899406097529/10191049462830330444178125000\) | \(-10191049462830330444178125000\) | \([6]\) | \(260112384\) | \(4.0777\) | |
| 257070.i7 | 257070i1 | \([1, 0, 1, -41747944, 71627679542]\) | \(8046906847713005637937400569/2440172914808194895155200\) | \(2440172914808194895155200\) | \([6]\) | \(65028096\) | \(3.3846\) | \(\Gamma_0(N)\)-optimal |
| 257070.i8 | 257070i8 | \([1, 0, 1, 4374468201, -92396036260934]\) | \(9257623277160554706885785873090711/9045445866485595703125000000000\) | \(-9045445866485595703125000000000\) | \([2]\) | \(780337152\) | \(4.6270\) |
Rank
sage: E.rank()
The elliptic curves in class 257070.i have rank \(0\).
Complex multiplication
The elliptic curves in class 257070.i do not have complex multiplication.Modular form 257070.2.a.i
sage: E.q_eigenform(10)
Isogeny matrix
sage: E.isogeny_class().matrix()
The \(i,j\) entry is the smallest degree of a cyclic isogeny between the \(i\)-th and \(j\)-th curve in the isogeny class, in the LMFDB numbering.
\(\left(\begin{array}{rrrrrrrr} 1 & 3 & 2 & 4 & 6 & 12 & 12 & 4 \\ 3 & 1 & 6 & 12 & 2 & 4 & 4 & 12 \\ 2 & 6 & 1 & 2 & 3 & 6 & 6 & 2 \\ 4 & 12 & 2 & 1 & 6 & 12 & 3 & 4 \\ 6 & 2 & 3 & 6 & 1 & 2 & 2 & 6 \\ 12 & 4 & 6 & 12 & 2 & 1 & 4 & 3 \\ 12 & 4 & 6 & 3 & 2 & 4 & 1 & 12 \\ 4 & 12 & 2 & 4 & 6 & 3 & 12 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
