Show commands:
SageMath
E = EllipticCurve("ha1")
E.isogeny_class()
Elliptic curves in class 114240ha
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 114240.dr2 | 114240ha1 | \([0, -1, 0, 5215, -174783]\) | \(59822347031/83966400\) | \(-22011287961600\) | \([2]\) | \(221184\) | \(1.2458\) | \(\Gamma_0(N)\)-optimal |
| 114240.dr1 | 114240ha2 | \([0, -1, 0, -33185, -1703103]\) | \(15417797707369/4080067320\) | \(1069565167534080\) | \([2]\) | \(442368\) | \(1.5924\) |
Rank
sage: E.rank()
The elliptic curves in class 114240ha have rank \(0\).
Complex multiplication
The elliptic curves in class 114240ha do not have complex multiplication.Modular form 114240.2.a.ha
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.
