Show commands:
SageMath
E = EllipticCurve("s1")
E.isogeny_class()
Elliptic curves in class 211185.s
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
211185.s1 | 211185q1 | \([0, 0, 1, -15162, -721910]\) | \(-303464448/1625\) | \(-2064138028875\) | \([]\) | \(331776\) | \(1.2075\) | \(\Gamma_0(N)\)-optimal |
211185.s2 | 211185q2 | \([0, 0, 1, 38988, -3842755]\) | \(7077888/10985\) | \(-10172154771817155\) | \([]\) | \(995328\) | \(1.7568\) |
Rank
sage: E.rank()
The elliptic curves in class 211185.s have rank \(1\).
Complex multiplication
The elliptic curves in class 211185.s do not have complex multiplication.Modular form 211185.2.a.s
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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.