Show commands:
SageMath
E = EllipticCurve("q1")
E.isogeny_class()
Elliptic curves in class 15680.q
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
15680.q1 | 15680w2 | \([0, 1, 0, -1241, -17081]\) | \(438976/5\) | \(2409451520\) | \([2]\) | \(11520\) | \(0.61348\) | |
15680.q2 | 15680w1 | \([0, 1, 0, -16, -666]\) | \(-64/25\) | \(-188238400\) | \([2]\) | \(5760\) | \(0.26691\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 15680.q have rank \(0\).
Complex multiplication
The elliptic curves in class 15680.q do not have complex multiplication.Modular form 15680.2.a.q
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.