Show commands:
SageMath
E = EllipticCurve("o1")
E.isogeny_class()
Elliptic curves in class 3696.o
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
3696.o1 | 3696o2 | \([0, -1, 0, -54, 291]\) | \(-1108671232/1369599\) | \(-21913584\) | \([]\) | \(864\) | \(0.10206\) | |
3696.o2 | 3696o1 | \([0, -1, 0, 6, -9]\) | \(1257728/2079\) | \(-33264\) | \([]\) | \(288\) | \(-0.44725\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 3696.o have rank \(1\).
Complex multiplication
The elliptic curves in class 3696.o do not have complex multiplication.Modular form 3696.2.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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.