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SageMath
E = EllipticCurve("e1")
E.isogeny_class()
Elliptic curves in class 47652e
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 47652.a2 | 47652e1 | \([0, -1, 0, -256069, -63651266]\) | \(-359661568/131769\) | \(-680323763978256816\) | \([2]\) | \(857280\) | \(2.1321\) | \(\Gamma_0(N)\)-optimal |
| 47652.a1 | 47652e2 | \([0, -1, 0, -4405764, -3557694456]\) | \(114489359728/9801\) | \(809641504238586624\) | \([2]\) | \(1714560\) | \(2.4787\) |
Rank
sage: E.rank()
The elliptic curves in class 47652e have rank \(1\).
Complex multiplication
The elliptic curves in class 47652e do not have complex multiplication.Modular form 47652.2.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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
