Show commands:
SageMath
E = EllipticCurve("o1")
E.isogeny_class()
Elliptic curves in class 35322.o
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
35322.o1 | 35322r2 | \([1, 0, 1, -19912, -1082986]\) | \(35796701971493/4572288\) | \(111513532032\) | \([2]\) | \(112896\) | \(1.1413\) | |
35322.o2 | 35322r1 | \([1, 0, 1, -1352, -13930]\) | \(11194326053/3096576\) | \(75522392064\) | \([2]\) | \(56448\) | \(0.79473\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 35322.o have rank \(0\).
Complex multiplication
The elliptic curves in class 35322.o do not have complex multiplication.Modular form 35322.2.a.o
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 LMFDB 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 LMFDB labels.