Show commands:
SageMath
E = EllipticCurve("by1")
E.isogeny_class()
Elliptic curves in class 439569by
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 439569.by1 | 439569by1 | \([1, -1, 0, -26163513, -51498053424]\) | \(23320116793/2873\) | \(244015153092164986857\) | \([2]\) | \(27869184\) | \(2.9354\) | \(\Gamma_0(N)\)-optimal |
| 439569.by2 | 439569by2 | \([1, -1, 0, -23965668, -60508778355]\) | \(-17923019113/8254129\) | \(-701055534833790007240161\) | \([2]\) | \(55738368\) | \(3.2819\) |
Rank
sage: E.rank()
The elliptic curves in class 439569by have rank \(0\).
Complex multiplication
The elliptic curves in class 439569by do not have complex multiplication.Modular form 439569.2.a.by
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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
