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SageMath
E = EllipticCurve("g1")
E.isogeny_class()
Elliptic curves in class 3400.g
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
3400.g1 | 3400c1 | \([0, -1, 0, -108, 212]\) | \(35152/17\) | \(68000000\) | \([2]\) | \(1024\) | \(0.19652\) | \(\Gamma_0(N)\)-optimal |
3400.g2 | 3400c2 | \([0, -1, 0, 392, 1212]\) | \(415292/289\) | \(-4624000000\) | \([2]\) | \(2048\) | \(0.54309\) |
Rank
sage: E.rank()
The elliptic curves in class 3400.g have rank \(1\).
Complex multiplication
The elliptic curves in class 3400.g do not have complex multiplication.Modular form 3400.2.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.