Show commands:
SageMath
E = EllipticCurve("j1")
E.isogeny_class()
Elliptic curves in class 485184.j
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
485184.j1 | 485184j1 | \([0, -1, 0, -7777, 449281]\) | \(-549754417/592704\) | \(-56089940852736\) | \([]\) | \(1244160\) | \(1.3331\) | \(\Gamma_0(N)\)-optimal |
485184.j2 | 485184j2 | \([0, -1, 0, 65183, -8087039]\) | \(323648023823/484243284\) | \(-45825871190163456\) | \([]\) | \(3732480\) | \(1.8824\) |
Rank
sage: E.rank()
The elliptic curves in class 485184.j have rank \(1\).
Complex multiplication
The elliptic curves in class 485184.j do not have complex multiplication.Modular form 485184.2.a.j
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.