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SageMath
E = EllipticCurve("g1")
E.isogeny_class()
Elliptic curves in class 1232.g
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
1232.g1 | 1232e2 | \([0, 0, 0, -355, -702]\) | \(2415899250/1294139\) | \(2650396672\) | \([2]\) | \(384\) | \(0.49939\) | |
1232.g2 | 1232e1 | \([0, 0, 0, 85, -86]\) | \(66325500/41503\) | \(-42499072\) | \([2]\) | \(192\) | \(0.15282\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 1232.g have rank \(1\).
Complex multiplication
The elliptic curves in class 1232.g do not have complex multiplication.Modular form 1232.2.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 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.