Show commands:
SageMath
E = EllipticCurve("b1")
E.isogeny_class()
Elliptic curves in class 388416b
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 388416.b2 | 388416b1 | \([0, -1, 0, -2779120, -1796507414]\) | \(-312770295872/2893401\) | \(-21959825948434963008\) | \([2]\) | \(15667200\) | \(2.5334\) | \(\Gamma_0(N)\)-optimal |
| 388416.b1 | 388416b2 | \([0, -1, 0, -44564185, -114490827719]\) | \(20150293992128/1701\) | \(826236837566042112\) | \([2]\) | \(31334400\) | \(2.8800\) |
Rank
sage: E.rank()
The elliptic curves in class 388416b have rank \(1\).
Complex multiplication
The elliptic curves in class 388416b do not have complex multiplication.Modular form 388416.2.a.b
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.
