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SageMath
E = EllipticCurve("dl1")
E.isogeny_class()
Elliptic curves in class 470890dl
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
470890.dl1 | 470890dl1 | \([1, -1, 1, -126552, 17359759]\) | \(-5154200289/20\) | \(-869753607380\) | \([]\) | \(3628800\) | \(1.5042\) | \(\Gamma_0(N)\)-optimal |
470890.dl2 | 470890dl2 | \([1, -1, 1, 882498, -164632499]\) | \(1747829720511/1280000000\) | \(-55664230872320000000\) | \([]\) | \(25401600\) | \(2.4771\) |
Rank
sage: E.rank()
The elliptic curves in class 470890dl have rank \(1\).
Complex multiplication
The elliptic curves in class 470890dl do not have complex multiplication.Modular form 470890.2.a.dl
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.