Show commands:
SageMath
E = EllipticCurve("s1")
E.isogeny_class()
Elliptic curves in class 6762.s
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
6762.s1 | 6762r1 | \([1, 0, 1, -15965, -777724]\) | \(1311889499494111/438012\) | \(150238116\) | \([2]\) | \(7680\) | \(0.92697\) | \(\Gamma_0(N)\)-optimal |
6762.s2 | 6762r2 | \([1, 0, 1, -15895, -784864]\) | \(-1294708239486271/23981814018\) | \(-8225762208174\) | \([2]\) | \(15360\) | \(1.2735\) |
Rank
sage: E.rank()
The elliptic curves in class 6762.s have rank \(0\).
Complex multiplication
The elliptic curves in class 6762.s do not have complex multiplication.Modular form 6762.2.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.