Show commands:
SageMath
E = EllipticCurve("a1")
E.isogeny_class()
Elliptic curves in class 90354a
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
90354.c4 | 90354a1 | \([1, 1, 0, -2766, -156]\) | \(912673/528\) | \(1354703543952\) | \([2]\) | \(202752\) | \(1.0174\) | \(\Gamma_0(N)\)-optimal |
90354.c2 | 90354a2 | \([1, 1, 0, -30146, -2020800]\) | \(1180932193/4356\) | \(11176304237604\) | \([2, 2]\) | \(405504\) | \(1.3639\) | |
90354.c3 | 90354a3 | \([1, 1, 0, -16456, -3847046]\) | \(-192100033/2371842\) | \(-6085497657375378\) | \([2]\) | \(811008\) | \(1.7105\) | |
90354.c1 | 90354a4 | \([1, 1, 0, -481916, -128968170]\) | \(4824238966273/66\) | \(169337942994\) | \([2]\) | \(811008\) | \(1.7105\) |
Rank
sage: E.rank()
The elliptic curves in class 90354a have rank \(1\).
Complex multiplication
The elliptic curves in class 90354a do not have complex multiplication.Modular form 90354.2.a.a
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.