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SageMath
E = EllipticCurve("v1")
E.isogeny_class()
Elliptic curves in class 350658.v
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
350658.v1 | 350658v1 | \([1, -1, 0, -135042, -16147180]\) | \(10395915890625/1698758656\) | \(44504203279269888\) | \([2]\) | \(3170304\) | \(1.9163\) | \(\Gamma_0(N)\)-optimal |
350658.v2 | 350658v2 | \([1, -1, 0, 245118, -90886636]\) | \(62169729933375/172005949696\) | \(-4506224426570135808\) | \([2]\) | \(6340608\) | \(2.2629\) |
Rank
sage: E.rank()
The elliptic curves in class 350658.v have rank \(2\).
Complex multiplication
The elliptic curves in class 350658.v do not have complex multiplication.Modular form 350658.2.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.