Show commands:
SageMath
E = EllipticCurve("c1")
E.isogeny_class()
Elliptic curves in class 690.c
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
690.c1 | 690c2 | \([1, 1, 0, -3172057, -2148591611]\) | \(3529773792266261468365081/50841342773437500000\) | \(50841342773437500000\) | \([2]\) | \(34560\) | \(2.5853\) | |
690.c2 | 690c1 | \([1, 1, 0, -22777, -90852059]\) | \(-1306902141891515161/3564268498800000000\) | \(-3564268498800000000\) | \([2]\) | \(17280\) | \(2.2387\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 690.c have rank \(0\).
Complex multiplication
The elliptic curves in class 690.c do not have complex multiplication.Modular form 690.2.a.c
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.