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SageMath
E = EllipticCurve("j1")
E.isogeny_class()
Elliptic curves in class 377520j
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 377520.j2 | 377520j1 | \([0, -1, 0, 578824, 583835760]\) | \(2955605685551/22016966400\) | \(-159762018355406438400\) | \([2]\) | \(10321920\) | \(2.5582\) | \(\Gamma_0(N)\)-optimal |
| 377520.j1 | 377520j2 | \([0, -1, 0, -7939576, 7889215600]\) | \(7627805994948049/711323149680\) | \(5161584027116545966080\) | \([2]\) | \(20643840\) | \(2.9048\) |
Rank
sage: E.rank()
The elliptic curves in class 377520j have rank \(1\).
Complex multiplication
The elliptic curves in class 377520j do not have complex multiplication.Modular form 377520.2.a.j
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.
