Show commands:
SageMath
E = EllipticCurve("ct1")
E.isogeny_class()
Elliptic curves in class 254100.ct
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
254100.ct1 | 254100ct2 | \([0, 1, 0, -6987548, 7104735108]\) | \(665567485783184/257298363\) | \(14586231848148576000\) | \([2]\) | \(10321920\) | \(2.6426\) | |
254100.ct2 | 254100ct1 | \([0, 1, 0, -371873, 145045008]\) | \(-1605176213504/1640558367\) | \(-5812698442401774000\) | \([2]\) | \(5160960\) | \(2.2960\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 254100.ct have rank \(2\).
Complex multiplication
The elliptic curves in class 254100.ct do not have complex multiplication.Modular form 254100.2.a.ct
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.