Show commands:
SageMath
E = EllipticCurve("z1")
E.isogeny_class()
Elliptic curves in class 170352z
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 170352.ci2 | 170352z1 | \([0, 0, 0, 17375397, -314979140086]\) | \(40251338884511/2997011332224\) | \(-43195248340621304850284544\) | \([]\) | \(37933056\) | \(3.5985\) | \(\Gamma_0(N)\)-optimal |
| 170352.ci1 | 170352z2 | \([0, 0, 0, -89422535163, -10292445612404566]\) | \(-5486773802537974663600129/2635437714\) | \(-37983969335876003241984\) | \([]\) | \(265531392\) | \(4.5715\) |
Rank
sage: E.rank()
The elliptic curves in class 170352z have rank \(0\).
Complex multiplication
The elliptic curves in class 170352z do not have complex multiplication.Modular form 170352.2.a.z
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.
\(\left(\begin{array}{rr} 1 & 7 \\ 7 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
