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SageMath
E = EllipticCurve("be1")
E.isogeny_class()
Elliptic curves in class 20808be
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 20808.o1 | 20808be1 | \([0, 0, 0, -125715, 16969502]\) | \(12194500/153\) | \(2756845602358272\) | \([2]\) | \(73728\) | \(1.7722\) | \(\Gamma_0(N)\)-optimal |
| 20808.o2 | 20808be2 | \([0, 0, 0, -21675, 44207174]\) | \(-31250/23409\) | \(-843594754321631232\) | \([2]\) | \(147456\) | \(2.1188\) |
Rank
sage: E.rank()
The elliptic curves in class 20808be have rank \(1\).
Complex multiplication
The elliptic curves in class 20808be do not have complex multiplication.Modular form 20808.2.a.be
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.
