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SageMath
E = EllipticCurve("ht1")
E.isogeny_class()
Elliptic curves in class 310464.ht
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
310464.ht1 | 310464ht2 | \([0, 0, 0, -8820, -318304]\) | \(5832000/11\) | \(143121420288\) | \([2]\) | \(368640\) | \(1.0306\) | |
310464.ht2 | 310464ht1 | \([0, 0, 0, -735, -1372]\) | \(216000/121\) | \(24598994112\) | \([2]\) | \(184320\) | \(0.68404\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 310464.ht have rank \(0\).
Complex multiplication
The elliptic curves in class 310464.ht do not have complex multiplication.Modular form 310464.2.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.