Show commands:
SageMath
E = EllipticCurve("d1")
E.isogeny_class()
Elliptic curves in class 17600d
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 17600.ca1 | 17600d1 | \([0, 1, 0, -141633, 20664863]\) | \(-76711450249/851840\) | \(-3489136640000000\) | \([]\) | \(129024\) | \(1.7972\) | \(\Gamma_0(N)\)-optimal |
| 17600.ca2 | 17600d2 | \([0, 1, 0, 474367, 107520863]\) | \(2882081488391/2883584000\) | \(-11811160064000000000\) | \([]\) | \(387072\) | \(2.3466\) |
Rank
sage: E.rank()
The elliptic curves in class 17600d have rank \(1\).
Complex multiplication
The elliptic curves in class 17600d do not have complex multiplication.Modular form 17600.2.a.d
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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
