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SageMath
E = EllipticCurve("e1")
E.isogeny_class()
Elliptic curves in class 630.e
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 630.e1 | 630b1 | \([1, -1, 0, -5124, 142160]\) | \(551105805571803/1376829440\) | \(37174394880\) | \([2]\) | \(1120\) | \(0.90561\) | \(\Gamma_0(N)\)-optimal |
| 630.e2 | 630b2 | \([1, -1, 0, -3204, 248528]\) | \(-134745327251163/903920796800\) | \(-24405861513600\) | \([2]\) | \(2240\) | \(1.2522\) |
Rank
sage: E.rank()
The elliptic curves in class 630.e have rank \(0\).
Complex multiplication
The elliptic curves in class 630.e do not have complex multiplication.Modular form 630.2.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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
