Show commands:
SageMath
E = EllipticCurve("w1")
E.isogeny_class()
Elliptic curves in class 79560.w
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
79560.w1 | 79560bn1 | \([0, 0, 0, -963, 2862]\) | \(132304644/71825\) | \(53617075200\) | \([2]\) | \(65536\) | \(0.74968\) | \(\Gamma_0(N)\)-optimal |
79560.w2 | 79560bn2 | \([0, 0, 0, 3717, 22518]\) | \(3804029838/2348125\) | \(-3505731840000\) | \([2]\) | \(131072\) | \(1.0963\) |
Rank
sage: E.rank()
The elliptic curves in class 79560.w have rank \(1\).
Complex multiplication
The elliptic curves in class 79560.w do not have complex multiplication.Modular form 79560.2.a.w
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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.