Show commands:
SageMath
E = EllipticCurve("ee1")
E.isogeny_class()
Elliptic curves in class 365904ee
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 365904.ee3 | 365904ee1 | \([0, 0, 0, 19965, 668162]\) | \(4492125/3584\) | \(-702178979217408\) | \([]\) | \(1244160\) | \(1.5367\) | \(\Gamma_0(N)\)-optimal |
| 365904.ee2 | 365904ee2 | \([0, 0, 0, -212355, -48227454]\) | \(-7414875/2744\) | \(-391914614322266112\) | \([]\) | \(3732480\) | \(2.0860\) | |
| 365904.ee1 | 365904ee3 | \([0, 0, 0, -18507555, -30645851742]\) | \(-545407363875/14\) | \(-17996079229083648\) | \([]\) | \(11197440\) | \(2.6353\) |
Rank
sage: E.rank()
The elliptic curves in class 365904ee have rank \(0\).
Complex multiplication
The elliptic curves in class 365904ee do not have complex multiplication.Modular form 365904.2.a.ee
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.
\(\left(\begin{array}{rrr} 1 & 3 & 9 \\ 3 & 1 & 3 \\ 9 & 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
