Show commands:
SageMath
E = EllipticCurve("c1")
E.isogeny_class()
Elliptic curves in class 471510.c
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 471510.c1 | 471510c1 | \([1, -1, 0, -20541891135, -1133200390041459]\) | \(7355650808184944781629532483/1274808911134720000\) | \(166137996389722201128960000\) | \([2]\) | \(939294720\) | \(4.4291\) | \(\Gamma_0(N)\)-optimal |
| 471510.c2 | 471510c2 | \([1, -1, 0, -20476995135, -1140716086655859]\) | \(-7286156838954742038925404483/96865758890419628262400\) | \(-12623917953710901837787380403200\) | \([2]\) | \(1878589440\) | \(4.7756\) |
Rank
sage: E.rank()
The elliptic curves in class 471510.c have rank \(0\).
Complex multiplication
The elliptic curves in class 471510.c do not have complex multiplication.Modular form 471510.2.a.c
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.
