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SageMath
E = EllipticCurve("dr1")
E.isogeny_class()
Elliptic curves in class 104400dr
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 104400.dy2 | 104400dr1 | \([0, 0, 0, -3675, 29610250]\) | \(-117649/8118144\) | \(-378760126464000000\) | \([]\) | \(752640\) | \(2.0519\) | \(\Gamma_0(N)\)-optimal |
| 104400.dy1 | 104400dr2 | \([0, 0, 0, -23439675, -43807049750]\) | \(-30526075007211889/103499257854\) | \(-4828861374436224000000\) | \([]\) | \(5268480\) | \(3.0248\) |
Rank
sage: E.rank()
The elliptic curves in class 104400dr have rank \(1\).
Complex multiplication
The elliptic curves in class 104400dr do not have complex multiplication.Modular form 104400.2.a.dr
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.
