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SageMath
E = EllipticCurve("e1")
E.isogeny_class()
Elliptic curves in class 9025.e
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 9025.e1 | 9025d2 | \([0, 1, 1, -7283, 175719]\) | \(7575076864/1953125\) | \(11016845703125\) | \([]\) | \(18144\) | \(1.2118\) | |
| 9025.e2 | 9025d1 | \([0, 1, 1, -2533, -49906]\) | \(318767104/125\) | \(705078125\) | \([]\) | \(6048\) | \(0.66249\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 9025.e have rank \(0\).
Complex multiplication
The elliptic curves in class 9025.e do not have complex multiplication.Modular form 9025.2.a.e
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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
