Show commands:
SageMath
E = EllipticCurve("i1")
E.isogeny_class()
Elliptic curves in class 23184.i
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
23184.i1 | 23184br2 | \([0, 0, 0, -36038091, 83266301050]\) | \(1733490909744055732873/99355964553216\) | \(296675320460470124544\) | \([2]\) | \(1622016\) | \(2.9919\) | |
23184.i2 | 23184br1 | \([0, 0, 0, -2123211, 1456827514]\) | \(-354499561600764553/101902222098432\) | \(-304278404750364377088\) | \([2]\) | \(811008\) | \(2.6454\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 23184.i have rank \(0\).
Complex multiplication
The elliptic curves in class 23184.i do not have complex multiplication.Modular form 23184.2.a.i
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.