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SageMath
E = EllipticCurve("ht1")
E.isogeny_class()
Elliptic curves in class 346560.ht
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
346560.ht1 | 346560ht2 | \([0, 1, 0, -693601, -219064801]\) | \(2992209121/54150\) | \(667820872472985600\) | \([2]\) | \(6635520\) | \(2.2155\) | |
346560.ht2 | 346560ht1 | \([0, 1, 0, -481, -9881185]\) | \(-1/3420\) | \(-42178160366714880\) | \([2]\) | \(3317760\) | \(1.8689\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 346560.ht have rank \(0\).
Complex multiplication
The elliptic curves in class 346560.ht do not have complex multiplication.Modular form 346560.2.a.ht
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.