Show commands:
SageMath
E = EllipticCurve("r1")
E.isogeny_class()
Elliptic curves in class 13520r
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 13520.h2 | 13520r1 | \([0, -1, 0, -180886, 28292315]\) | \(296747776/15625\) | \(34464622962250000\) | \([]\) | \(89856\) | \(1.9302\) | \(\Gamma_0(N)\)-optimal |
| 13520.h1 | 13520r2 | \([0, -1, 0, -14461386, 21172000615]\) | \(151635187115776/25\) | \(55143396739600\) | \([]\) | \(269568\) | \(2.4795\) |
Rank
sage: E.rank()
The elliptic curves in class 13520r have rank \(0\).
Complex multiplication
The elliptic curves in class 13520r do not have complex multiplication.Modular form 13520.2.a.r
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.
