Show commands:
SageMath
E = EllipticCurve("be1")
E.isogeny_class()
Elliptic curves in class 139425be
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 139425.r1 | 139425be1 | \([0, -1, 1, -3943, 101298]\) | \(-56197120/3267\) | \(-394229625075\) | \([]\) | \(168480\) | \(0.98126\) | \(\Gamma_0(N)\)-optimal |
| 139425.r2 | 139425be2 | \([0, -1, 1, 21407, 169743]\) | \(8990228480/5314683\) | \(-641323993413675\) | \([]\) | \(505440\) | \(1.5306\) |
Rank
sage: E.rank()
The elliptic curves in class 139425be have rank \(0\).
Complex multiplication
The elliptic curves in class 139425be do not have complex multiplication.Modular form 139425.2.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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
