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SageMath
E = EllipticCurve("g1")
E.isogeny_class()
Elliptic curves in class 1694.g
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
1694.g1 | 1694g2 | \([1, -1, 1, -56772, -5192305]\) | \(11422548526761/4312\) | \(7638971032\) | \([2]\) | \(5760\) | \(1.2470\) | |
1694.g2 | 1694g1 | \([1, -1, 1, -3532, -81265]\) | \(-2749884201/54208\) | \(-96032778688\) | \([2]\) | \(2880\) | \(0.90039\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 1694.g have rank \(0\).
Complex multiplication
The elliptic curves in class 1694.g do not have complex multiplication.Modular form 1694.2.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.