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SageMath
E = EllipticCurve("g1")
E.isogeny_class()
Elliptic curves in class 1216.g
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
1216.g1 | 1216j2 | \([0, -1, 0, -4481, 129313]\) | \(-37966934881/4952198\) | \(-1298188992512\) | \([]\) | \(1920\) | \(1.0575\) | |
1216.g2 | 1216j1 | \([0, -1, 0, -1, -607]\) | \(-1/608\) | \(-159383552\) | \([]\) | \(384\) | \(0.25279\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 1216.g have rank \(0\).
Complex multiplication
The elliptic curves in class 1216.g do not have complex multiplication.Modular form 1216.2.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.
\(\left(\begin{array}{rr} 1 & 5 \\ 5 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.