Show commands:
SageMath
E = EllipticCurve("n1")
E.isogeny_class()
Elliptic curves in class 92510n
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
92510.p1 | 92510n1 | \([1, 1, 1, -74446, 7861899]\) | \(-76711450249/851840\) | \(-506694297760640\) | \([]\) | \(698544\) | \(1.6365\) | \(\Gamma_0(N)\)-optimal |
92510.p2 | 92510n2 | \([1, 1, 1, 249339, 41017483]\) | \(2882081488391/2883584000\) | \(-1715223011262464000\) | \([]\) | \(2095632\) | \(2.1858\) |
Rank
sage: E.rank()
The elliptic curves in class 92510n have rank \(0\).
Complex multiplication
The elliptic curves in class 92510n do not have complex multiplication.Modular form 92510.2.a.n
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 Cremona 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 Cremona labels.