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SageMath
E = EllipticCurve("w1")
E.isogeny_class()
Elliptic curves in class 57498w
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
57498.q2 | 57498w1 | \([1, 0, 0, 6021, 243729]\) | \(476562552731/780337152\) | \(-39526417760256\) | \([2]\) | \(138240\) | \(1.2941\) | \(\Gamma_0(N)\)-optimal |
57498.q1 | 57498w2 | \([1, 0, 0, -41339, 2488593]\) | \(154240738777189/36294822144\) | \(1838441626060032\) | \([2]\) | \(276480\) | \(1.6407\) |
Rank
sage: E.rank()
The elliptic curves in class 57498w have rank \(1\).
Complex multiplication
The elliptic curves in class 57498w do not have complex multiplication.Modular form 57498.2.a.w
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 Cremona 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 Cremona labels.