Show commands:
SageMath
E = EllipticCurve("f1")
E.isogeny_class()
Elliptic curves in class 70262f
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 70262.g2 | 70262f1 | \([1, 1, 1, -28698, -1883777]\) | \(-413493625/152\) | \(-960847183448\) | \([]\) | \(157248\) | \(1.2672\) | \(\Gamma_0(N)\)-optimal |
| 70262.g3 | 70262f2 | \([1, 1, 1, 17527, -7105353]\) | \(94196375/3511808\) | \(-22199413326382592\) | \([]\) | \(471744\) | \(1.8165\) | |
| 70262.g1 | 70262f3 | \([1, 1, 1, -158128, 194616849]\) | \(-69173457625/2550136832\) | \(-16120340739698720768\) | \([]\) | \(1415232\) | \(2.3658\) |
Rank
sage: E.rank()
The elliptic curves in class 70262f have rank \(1\).
Complex multiplication
The elliptic curves in class 70262f do not have complex multiplication.Modular form 70262.2.a.f
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.
