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SageMath
E = EllipticCurve("v1")
E.isogeny_class()
Elliptic curves in class 37026.v
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
37026.v1 | 37026be1 | \([1, -1, 1, -213467, -37884085]\) | \(832972004929/610368\) | \(788270721302592\) | \([2]\) | \(368640\) | \(1.7926\) | \(\Gamma_0(N)\)-optimal |
37026.v2 | 37026be2 | \([1, -1, 1, -169907, -53827045]\) | \(-420021471169/727634952\) | \(-939717233632852488\) | \([2]\) | \(737280\) | \(2.1392\) |
Rank
sage: E.rank()
The elliptic curves in class 37026.v have rank \(0\).
Complex multiplication
The elliptic curves in class 37026.v do not have complex multiplication.Modular form 37026.2.a.v
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.