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SageMath
E = EllipticCurve("be1")
E.isogeny_class()
Elliptic curves in class 139425.be
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 139425.be1 | 139425u1 | \([0, 1, 1, -98583, 12465119]\) | \(-56197120/3267\) | \(-6159837891796875\) | \([]\) | \(842400\) | \(1.7860\) | \(\Gamma_0(N)\)-optimal |
| 139425.be2 | 139425u2 | \([0, 1, 1, 535167, 22288244]\) | \(8990228480/5314683\) | \(-10020687397088671875\) | \([]\) | \(2527200\) | \(2.3353\) |
Rank
sage: E.rank()
The elliptic curves in class 139425.be have rank \(0\).
Complex multiplication
The elliptic curves in class 139425.be 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 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.
