Show commands:
SageMath
E = EllipticCurve("a1")
E.isogeny_class()
Elliptic curves in class 262080.a
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
262080.a1 | 262080a1 | \([0, 0, 0, -948, -1888]\) | \(31554496/17745\) | \(52986286080\) | \([2]\) | \(245760\) | \(0.74789\) | \(\Gamma_0(N)\)-optimal |
262080.a2 | 262080a2 | \([0, 0, 0, 3732, -14992]\) | \(240641848/143325\) | \(-3423729254400\) | \([2]\) | \(491520\) | \(1.0945\) |
Rank
sage: E.rank()
The elliptic curves in class 262080.a have rank \(2\).
Complex multiplication
The elliptic curves in class 262080.a do not have complex multiplication.Modular form 262080.2.a.a
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.