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SageMath
E = EllipticCurve("j1")
E.isogeny_class()
Elliptic curves in class 93058j
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 93058.k2 | 93058j1 | \([1, -1, 1, -810555, 281069483]\) | \(2439928775390625/137331712\) | \(3314853674288128\) | \([2]\) | \(829440\) | \(2.0427\) | \(\Gamma_0(N)\)-optimal |
| 93058.k1 | 93058j2 | \([1, -1, 1, -856795, 247240299]\) | \(2881777717022625/575561496608\) | \(13892655338118865952\) | \([2]\) | \(1658880\) | \(2.3893\) |
Rank
sage: E.rank()
The elliptic curves in class 93058j have rank \(1\).
Complex multiplication
The elliptic curves in class 93058j do not have complex multiplication.Modular form 93058.2.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.
