Show commands:
SageMath
E = EllipticCurve("l1")
E.isogeny_class()
Elliptic curves in class 289800.l
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
289800.l1 | 289800l4 | \([0, 0, 0, -21891657675, 1093451708915750]\) | \(49737293673675178002921218/6641736806881023047235\) | \(154938436230920505645898080000000\) | \([2]\) | \(849346560\) | \(4.9044\) | |
289800.l2 | 289800l2 | \([0, 0, 0, -21135342675, 1182643180550750]\) | \(89516703758060574923008036/1985322833430374025\) | \(23156805529131882627600000000\) | \([2, 2]\) | \(424673280\) | \(4.5578\) | |
289800.l3 | 289800l1 | \([0, 0, 0, -21135230175, 1182656400313250]\) | \(358061097267989271289240144/176126855625\) | \(513585911002500000000\) | \([2]\) | \(212336640\) | \(4.2112\) | \(\Gamma_0(N)\)-optimal |
289800.l4 | 289800l3 | \([0, 0, 0, -20380827675, 1270988587385750]\) | \(-40133926989810174413190818/6689384645060302103835\) | \(-156049964999966727478262880000000\) | \([2]\) | \(849346560\) | \(4.9044\) |
Rank
sage: E.rank()
The elliptic curves in class 289800.l have rank \(1\).
Complex multiplication
The elliptic curves in class 289800.l do not have complex multiplication.Modular form 289800.2.a.l
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.