Show commands:
SageMath
E = EllipticCurve("dv1")
E.isogeny_class()
Elliptic curves in class 102960.dv
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 102960.dv1 | 102960ck1 | \([0, 0, 0, -159747, -709103614]\) | \(-4076600308125723/1961812478912000\) | \(-216960765667835904000\) | \([]\) | \(2612736\) | \(2.5813\) | \(\Gamma_0(N)\)-optimal |
| 102960.dv2 | 102960ck2 | \([0, 0, 0, 1437453, 19125671346]\) | \(4074304020054813/1962402098708480\) | \(-158211934244368432496640\) | \([]\) | \(7838208\) | \(3.1306\) |
Rank
sage: E.rank()
The elliptic curves in class 102960.dv have rank \(0\).
Complex multiplication
The elliptic curves in class 102960.dv do not have complex multiplication.Modular form 102960.2.a.dv
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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
