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SageMath
E = EllipticCurve("g1")
E.isogeny_class()
Elliptic curves in class 3366.g
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
3366.g1 | 3366d1 | \([1, -1, 0, -1782, -28512]\) | \(858729462625/38148\) | \(27809892\) | \([2]\) | \(2048\) | \(0.50573\) | \(\Gamma_0(N)\)-optimal |
3366.g2 | 3366d2 | \([1, -1, 0, -1692, -31590]\) | \(-735091890625/181908738\) | \(-132611470002\) | \([2]\) | \(4096\) | \(0.85230\) |
Rank
sage: E.rank()
The elliptic curves in class 3366.g have rank \(1\).
Complex multiplication
The elliptic curves in class 3366.g do not have complex multiplication.Modular form 3366.2.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.