Show commands:
SageMath
E = EllipticCurve("s1")
E.isogeny_class()
Elliptic curves in class 242592.s
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
242592.s1 | 242592s2 | \([0, -1, 0, -12033, 483633]\) | \(1000000/63\) | \(12140095500288\) | \([2]\) | \(442368\) | \(1.2617\) | |
242592.s2 | 242592s1 | \([0, -1, 0, 602, 31300]\) | \(8000/147\) | \(-442607648448\) | \([2]\) | \(221184\) | \(0.91510\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 242592.s have rank \(1\).
Complex multiplication
The elliptic curves in class 242592.s do not have complex multiplication.Modular form 242592.2.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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.