Show commands:
SageMath
E = EllipticCurve("be1")
E.isogeny_class()
Elliptic curves in class 7098.be
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 7098.be1 | 7098bd3 | \([1, 0, 0, -330652, 73139780]\) | \(828279937799497/193444524\) | \(933719769443916\) | \([2]\) | \(64512\) | \(1.8631\) | |
| 7098.be2 | 7098bd2 | \([1, 0, 0, -23072, 858480]\) | \(281397674377/96589584\) | \(466219473357456\) | \([2, 2]\) | \(32256\) | \(1.5165\) | |
| 7098.be3 | 7098bd1 | \([1, 0, 0, -9552, -350208]\) | \(19968681097/628992\) | \(3036024246528\) | \([2]\) | \(16128\) | \(1.1700\) | \(\Gamma_0(N)\)-optimal |
| 7098.be4 | 7098bd4 | \([1, 0, 0, 68188, 5987292]\) | \(7264187703863/7406095788\) | \(-35747809804380492\) | \([2]\) | \(64512\) | \(1.8631\) |
Rank
sage: E.rank()
The elliptic curves in class 7098.be have rank \(0\).
Complex multiplication
The elliptic curves in class 7098.be do not have complex multiplication.Modular form 7098.2.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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
