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SageMath
E = EllipticCurve("g1")
E.isogeny_class()
Elliptic curves in class 102960.g
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
102960.g1 | 102960cd2 | \([0, 0, 0, -2027403, 1111113018]\) | \(11431223764109163/148720\) | \(11990039592960\) | \([2]\) | \(1474560\) | \(2.0687\) | |
102960.g2 | 102960cd1 | \([0, 0, 0, -126603, 17392698]\) | \(-2783584838763/10067200\) | \(-811633449369600\) | \([2]\) | \(737280\) | \(1.7221\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 102960.g have rank \(1\).
Complex multiplication
The elliptic curves in class 102960.g do not have complex multiplication.Modular form 102960.2.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.