Show commands:
SageMath
E = EllipticCurve("r1")
E.isogeny_class()
Elliptic curves in class 58989r
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
58989.l2 | 58989r1 | \([0, 1, 1, -2183529, 1240634774]\) | \(18492424192/9261\) | \(576586992899614221\) | \([3]\) | \(1167696\) | \(2.3606\) | \(\Gamma_0(N)\)-optimal |
58989.l1 | 58989r2 | \([0, 1, 1, -6649839, -5112691201]\) | \(522336305152/121060821\) | \(7537209236405190387381\) | \([]\) | \(3503088\) | \(2.9099\) |
Rank
sage: E.rank()
The elliptic curves in class 58989r have rank \(0\).
Complex multiplication
The elliptic curves in class 58989r do not have complex multiplication.Modular form 58989.2.a.r
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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.