Show commands:
SageMath
E = EllipticCurve("d1")
E.isogeny_class()
Elliptic curves in class 314330.d
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
314330.d1 | 314330d2 | \([1, 1, 0, -12279247, 17090604581]\) | \(-32391289681150609/1228250000000\) | \(-7764214164934250000000\) | \([]\) | \(19432224\) | \(2.9704\) | |
314330.d2 | 314330d1 | \([1, 1, 0, 737713, 76017829]\) | \(7023836099951/4456448000\) | \(-28170825716989952000\) | \([]\) | \(6477408\) | \(2.4211\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 314330.d have rank \(1\).
Complex multiplication
The elliptic curves in class 314330.d do not have complex multiplication.Modular form 314330.2.a.d
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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.