Show commands:
SageMath
E = EllipticCurve("i1")
E.isogeny_class()
Elliptic curves in class 2940i
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
2940.g1 | 2940i1 | \([0, 1, 0, -27701, -1783776]\) | \(1248870793216/42525\) | \(80048379600\) | \([2]\) | \(5760\) | \(1.1838\) | \(\Gamma_0(N)\)-optimal |
2940.g2 | 2940i2 | \([0, 1, 0, -26476, -1947436]\) | \(-68150496976/14467005\) | \(-435719339838720\) | \([2]\) | \(11520\) | \(1.5304\) |
Rank
sage: E.rank()
The elliptic curves in class 2940i have rank \(0\).
Complex multiplication
The elliptic curves in class 2940i do not have complex multiplication.Modular form 2940.2.a.i
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.