Show commands:
SageMath
E = EllipticCurve("hv1")
E.isogeny_class()
Elliptic curves in class 122304hv
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 122304.go2 | 122304hv1 | \([0, 1, 0, -408, -1254]\) | \(1000000/507\) | \(3817474752\) | \([2]\) | \(46080\) | \(0.53107\) | \(\Gamma_0(N)\)-optimal |
| 122304.go1 | 122304hv2 | \([0, 1, 0, -3593, 80919]\) | \(10648000/117\) | \(56381165568\) | \([2]\) | \(92160\) | \(0.87764\) |
Rank
sage: E.rank()
The elliptic curves in class 122304hv have rank \(1\).
Complex multiplication
The elliptic curves in class 122304hv do not have complex multiplication.Modular form 122304.2.a.hv
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.
