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SageMath
E = EllipticCurve("f1")
E.isogeny_class()
Elliptic curves in class 114582f
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
114582.h2 | 114582f1 | \([1, 0, 1, -280713, 57615820]\) | \(-506814405937489/4048994304\) | \(-19543722147495936\) | \([]\) | \(889056\) | \(1.9540\) | \(\Gamma_0(N)\)-optimal |
114582.h1 | 114582f2 | \([1, 0, 1, -1203453, -5639380940]\) | \(-39934705050538129/2823126576537804\) | \(-13626692767771861187436\) | \([]\) | \(6223392\) | \(2.9269\) |
Rank
sage: E.rank()
The elliptic curves in class 114582f have rank \(1\).
Complex multiplication
The elliptic curves in class 114582f do not have complex multiplication.Modular form 114582.2.a.f
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.
\(\left(\begin{array}{rr} 1 & 7 \\ 7 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.