Show commands:
SageMath
E = EllipticCurve("s1")
E.isogeny_class()
Elliptic curves in class 8280.s
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
8280.s1 | 8280r1 | \([0, 0, 0, -162, -459]\) | \(1492992/575\) | \(181083600\) | \([2]\) | \(2688\) | \(0.28359\) | \(\Gamma_0(N)\)-optimal |
8280.s2 | 8280r2 | \([0, 0, 0, 513, -3294]\) | \(2963088/2645\) | \(-13327752960\) | \([2]\) | \(5376\) | \(0.63017\) |
Rank
sage: E.rank()
The elliptic curves in class 8280.s have rank \(0\).
Complex multiplication
The elliptic curves in class 8280.s do not have complex multiplication.Modular form 8280.2.a.s
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.