Show commands:
SageMath
E = EllipticCurve("d1")
E.isogeny_class()
Elliptic curves in class 254100d
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
254100.d2 | 254100d1 | \([0, -1, 0, 807, 20682]\) | \(16384/63\) | \(-223216686000\) | \([2]\) | \(245760\) | \(0.86039\) | \(\Gamma_0(N)\)-optimal |
254100.d1 | 254100d2 | \([0, -1, 0, -8268, 256632]\) | \(1102736/147\) | \(8333422944000\) | \([2]\) | \(491520\) | \(1.2070\) |
Rank
sage: E.rank()
The elliptic curves in class 254100d have rank \(2\).
Complex multiplication
The elliptic curves in class 254100d do not have complex multiplication.Modular form 254100.2.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 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.