Show commands:
SageMath
E = EllipticCurve("l1")
E.isogeny_class()
Elliptic curves in class 2736l
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
2736.f2 | 2736l1 | \([0, 0, 0, -51, -14]\) | \(132651/76\) | \(8404992\) | \([2]\) | \(384\) | \(0.018388\) | \(\Gamma_0(N)\)-optimal |
2736.f1 | 2736l2 | \([0, 0, 0, -531, 4690]\) | \(149721291/722\) | \(79847424\) | \([2]\) | \(768\) | \(0.36496\) |
Rank
sage: E.rank()
The elliptic curves in class 2736l have rank \(1\).
Complex multiplication
The elliptic curves in class 2736l do not have complex multiplication.Modular form 2736.2.a.l
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 Cremona 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 Cremona labels.