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SageMath
E = EllipticCurve("e1")
E.isogeny_class()
Elliptic curves in class 30634e
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 30634.f2 | 30634e1 | \([1, 1, 1, -81793, -11468673]\) | \(-2507141976625/889192448\) | \(-21462944067878912\) | \([]\) | \(241920\) | \(1.8447\) | \(\Gamma_0(N)\)-optimal |
| 30634.f1 | 30634e2 | \([1, 1, 1, -7110273, -7300520321]\) | \(-1646982616152408625/38112512\) | \(-919943388163328\) | \([]\) | \(725760\) | \(2.3940\) |
Rank
sage: E.rank()
The elliptic curves in class 30634e have rank \(0\).
Complex multiplication
The elliptic curves in class 30634e do not have complex multiplication.Modular form 30634.2.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 Cremona 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 Cremona labels.
