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SageMath
E = EllipticCurve("cw1")
E.isogeny_class()
Elliptic curves in class 25410.cw
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 25410.cw1 | 25410cx4 | \([1, 0, 0, -32199615, -70330013775]\) | \(2084105208962185000201/31185000\) | \(55246129785000\) | \([2]\) | \(1474560\) | \(2.6405\) | |
| 25410.cw2 | 25410cx3 | \([1, 0, 0, -2181935, -903104223]\) | \(648474704552553481/176469171805080\) | \(312625902472179329880\) | \([2]\) | \(1474560\) | \(2.6405\) | |
| 25410.cw3 | 25410cx2 | \([1, 0, 0, -2012535, -1098964503]\) | \(508859562767519881/62240270400\) | \(110262435670094400\) | \([2, 2]\) | \(737280\) | \(2.2939\) | |
| 25410.cw4 | 25410cx1 | \([1, 0, 0, -115255, -20171095]\) | \(-95575628340361/43812679680\) | \(-77616834626580480\) | \([4]\) | \(368640\) | \(1.9473\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 25410.cw have rank \(0\).
Complex multiplication
The elliptic curves in class 25410.cw do not have complex multiplication.Modular form 25410.2.a.cw
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.
\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
