Show commands:
SageMath
E = EllipticCurve("d1")
E.isogeny_class()
Elliptic curves in class 378.d
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 378.d1 | 378b3 | \([1, -1, 0, -1062, 13590]\) | \(-545407363875/14\) | \(-3402\) | \([3]\) | \(108\) | \(0.19388\) | |
| 378.d2 | 378b1 | \([1, -1, 0, -12, 24]\) | \(-7414875/2744\) | \(-74088\) | \([3]\) | \(36\) | \(-0.35542\) | \(\Gamma_0(N)\)-optimal |
| 378.d3 | 378b2 | \([1, -1, 0, 93, -235]\) | \(4492125/3584\) | \(-70543872\) | \([]\) | \(108\) | \(0.19388\) |
Rank
sage: E.rank()
The elliptic curves in class 378.d have rank \(0\).
Complex multiplication
The elliptic curves in class 378.d do not have complex multiplication.Modular form 378.2.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.
\(\left(\begin{array}{rrr} 1 & 3 & 9 \\ 3 & 1 & 3 \\ 9 & 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
