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SageMath
E = EllipticCurve("q1")
E.isogeny_class()
Elliptic curves in class 24150.q
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 24150.q1 | 24150p6 | \([1, 1, 0, -5598936000, -161254800202500]\) | \(1242282009445982549834550082561/41992020\) | \(656125312500\) | \([2]\) | \(9437184\) | \(3.6872\) | |
| 24150.q2 | 24150p4 | \([1, 1, 0, -349933500, -2519715600000]\) | \(303291507481995500913332161/1763329743680400\) | \(27552027245006250000\) | \([2, 2]\) | \(4718592\) | \(3.3406\) | |
| 24150.q3 | 24150p5 | \([1, 1, 0, -349731000, -2522777197500]\) | \(-302765284673144739899429761/731344538939408411220\) | \(-11427258420928256425312500\) | \([4]\) | \(9437184\) | \(3.6872\) | |
| 24150.q4 | 24150p2 | \([1, 1, 0, -21883500, -39329550000]\) | \(74174404299602673044161/178530248806560000\) | \(2789535137602500000000\) | \([2, 2]\) | \(2359296\) | \(2.9940\) | |
| 24150.q5 | 24150p3 | \([1, 1, 0, -13833500, -68623500000]\) | \(-18736995756767139956161/119334500162058560400\) | \(-1864601565032165006250000\) | \([2]\) | \(4718592\) | \(3.3406\) | |
| 24150.q6 | 24150p1 | \([1, 1, 0, -1883500, -109550000]\) | \(47293441677949844161/27041817600000000\) | \(422528400000000000000\) | \([2]\) | \(1179648\) | \(2.6475\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 24150.q have rank \(1\).
Complex multiplication
The elliptic curves in class 24150.q do not have complex multiplication.Modular form 24150.2.a.q
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.
\(\left(\begin{array}{rrrrrr} 1 & 2 & 4 & 4 & 8 & 8 \\ 2 & 1 & 2 & 2 & 4 & 4 \\ 4 & 2 & 1 & 4 & 8 & 8 \\ 4 & 2 & 4 & 1 & 2 & 2 \\ 8 & 4 & 8 & 2 & 1 & 4 \\ 8 & 4 & 8 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
