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SageMath
E = EllipticCurve("if1")
E.isogeny_class()
Elliptic curves in class 284592.if
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 284592.if1 | 284592if1 | \([0, 1, 0, -49408, -1267708]\) | \(62500/33\) | \(7043009067967488\) | \([2]\) | \(1382400\) | \(1.7325\) | \(\Gamma_0(N)\)-optimal |
| 284592.if2 | 284592if2 | \([0, 1, 0, 187752, -9710604]\) | \(1714750/1089\) | \(-464838598485854208\) | \([2]\) | \(2764800\) | \(2.0790\) |
Rank
sage: E.rank()
The elliptic curves in class 284592.if have rank \(0\).
Complex multiplication
The elliptic curves in class 284592.if do not have complex multiplication.Modular form 284592.2.a.if
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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
