Show commands:
SageMath
E = EllipticCurve("be1")
E.isogeny_class()
Elliptic curves in class 23120.be
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 23120.be1 | 23120be2 | \([0, 1, 0, -30708080, 67599430100]\) | \(-32391289681150609/1228250000000\) | \(-121433985532928000000000\) | \([]\) | \(1741824\) | \(3.1995\) | |
| 23120.be2 | 23120be1 | \([0, 1, 0, 1844880, 300032468]\) | \(7023836099951/4456448000\) | \(-440597795204759552000\) | \([]\) | \(580608\) | \(2.6502\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 23120.be have rank \(1\).
Complex multiplication
The elliptic curves in class 23120.be do not have complex multiplication.Modular form 23120.2.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 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.
