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SageMath
E = EllipticCurve("m1")
E.isogeny_class()
Elliptic curves in class 14490m
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 14490.b6 | 14490m1 | \([1, -1, 0, -678060, 23662800]\) | \(47293441677949844161/27041817600000000\) | \(19713485030400000000\) | \([2]\) | \(393216\) | \(2.3921\) | \(\Gamma_0(N)\)-optimal |
| 14490.b4 | 14490m2 | \([1, -1, 0, -7878060, 8495182800]\) | \(74174404299602673044161/178530248806560000\) | \(130148551379982240000\) | \([2, 2]\) | \(786432\) | \(2.7386\) | |
| 14490.b2 | 14490m3 | \([1, -1, 0, -125976060, 544258569600]\) | \(303291507481995500913332161/1763329743680400\) | \(1285467383143011600\) | \([2, 2]\) | \(1572864\) | \(3.0852\) | |
| 14490.b5 | 14490m4 | \([1, -1, 0, -4980060, 14822676000]\) | \(-18736995756767139956161/119334500162058560400\) | \(-86994850618140690531600\) | \([2]\) | \(1572864\) | \(3.0852\) | |
| 14490.b1 | 14490m5 | \([1, -1, 0, -2015616960, 34831036843740]\) | \(1242282009445982549834550082561/41992020\) | \(30612182580\) | \([2]\) | \(3145728\) | \(3.4318\) | |
| 14490.b3 | 14490m6 | \([1, -1, 0, -125903160, 544919874660]\) | \(-302765284673144739899429761/731344538939408411220\) | \(-533150168886828731779380\) | \([2]\) | \(3145728\) | \(3.4318\) |
Rank
sage: E.rank()
The elliptic curves in class 14490m have rank \(1\).
Complex multiplication
The elliptic curves in class 14490m do not have complex multiplication.Modular form 14490.2.a.m
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 Cremona numbering.
\(\left(\begin{array}{rrrrrr} 1 & 2 & 4 & 4 & 8 & 8 \\ 2 & 1 & 2 & 2 & 4 & 4 \\ 4 & 2 & 1 & 4 & 2 & 2 \\ 4 & 2 & 4 & 1 & 8 & 8 \\ 8 & 4 & 2 & 8 & 1 & 4 \\ 8 & 4 & 2 & 8 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
