Show commands:
SageMath
E = EllipticCurve("i1")
E.isogeny_class()
Elliptic curves in class 79560.i
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 79560.i1 | 79560q2 | \([0, 0, 0, -74566426143, 7834666270861042]\) | \(245689277968779868090419995701456/93342399137270122585475925\) | \(17419931896593899357391859027200\) | \([2]\) | \(247726080\) | \(4.9608\) | |
| 79560.i2 | 79560q1 | \([0, 0, 0, -3974344518, 159711617178817]\) | \(-595213448747095198927846967296/600281130562949295663181875\) | \(-7001679106886240584615353390000\) | \([2]\) | \(123863040\) | \(4.6143\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 79560.i have rank \(0\).
Complex multiplication
The elliptic curves in class 79560.i do not have complex multiplication.Modular form 79560.2.a.i
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.
