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SageMath
E = EllipticCurve("g1")
E.isogeny_class()
Elliptic curves in class 3640.g
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
3640.g1 | 3640b1 | \([0, -1, 0, -3596, 84116]\) | \(20093868785104/26374985\) | \(6751996160\) | \([2]\) | \(3840\) | \(0.79278\) | \(\Gamma_0(N)\)-optimal |
3640.g2 | 3640b2 | \([0, -1, 0, -2616, 129980]\) | \(-1934207124196/5912841025\) | \(-6054749209600\) | \([2]\) | \(7680\) | \(1.1394\) |
Rank
sage: E.rank()
The elliptic curves in class 3640.g have rank \(1\).
Complex multiplication
The elliptic curves in class 3640.g do not have complex multiplication.Modular form 3640.2.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.