Show commands:
SageMath
E = EllipticCurve("e1")
E.isogeny_class()
Elliptic curves in class 96192e
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 96192.v2 | 96192e1 | \([0, 0, 0, 1356, -21728]\) | \(92345408/121743\) | \(-363522650112\) | \([2]\) | \(86016\) | \(0.90411\) | \(\Gamma_0(N)\)-optimal |
| 96192.v1 | 96192e2 | \([0, 0, 0, -8364, -212240]\) | \(2708870984/753003\) | \(17987639279616\) | \([2]\) | \(172032\) | \(1.2507\) |
Rank
sage: E.rank()
The elliptic curves in class 96192e have rank \(0\).
Complex multiplication
The elliptic curves in class 96192e do not have complex multiplication.Modular form 96192.2.a.e
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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
