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SageMath
E = EllipticCurve("g1")
E.isogeny_class()
Elliptic curves in class 414736g
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 414736.g2 | 414736g1 | \([0, 1, 0, -2186004, 816925276]\) | \(21296/7\) | \(379731626567481192704\) | \([2]\) | \(11870208\) | \(2.6518\) | \(\Gamma_0(N)\)-optimal |
| 414736.g1 | 414736g2 | \([0, 1, 0, -14109664, -19791928668]\) | \(1431644/49\) | \(10632485543889473395712\) | \([2]\) | \(23740416\) | \(2.9984\) |
Rank
sage: E.rank()
The elliptic curves in class 414736g have rank \(1\).
Complex multiplication
The elliptic curves in class 414736g do not have complex multiplication.Modular form 414736.2.a.g
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.
