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SageMath
E = EllipticCurve("e1")
E.isogeny_class()
Elliptic curves in class 735.e
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 735.e1 | 735d2 | \([0, 1, 1, -10061, -392605]\) | \(-19539165184/46875\) | \(-270225046875\) | \([]\) | \(1008\) | \(1.0729\) | |
| 735.e2 | 735d1 | \([0, 1, 1, 229, -2614]\) | \(229376/675\) | \(-3891240675\) | \([3]\) | \(336\) | \(0.52357\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 735.e have rank \(0\).
Complex multiplication
The elliptic curves in class 735.e do not have complex multiplication.Modular form 735.2.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.
