Show commands:
SageMath
E = EllipticCurve("v1")
E.isogeny_class()
Elliptic curves in class 58190.v
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
58190.v1 | 58190p2 | \([1, 1, 1, -3142271, 2142635523]\) | \(-23178622194826561/1610510\) | \(-238413279593390\) | \([]\) | \(1188000\) | \(2.2128\) | |
58190.v2 | 58190p1 | \([1, 1, 1, 5279, 598143]\) | \(109902239/1100000\) | \(-162839477900000\) | \([]\) | \(237600\) | \(1.4081\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 58190.v have rank \(1\).
Complex multiplication
The elliptic curves in class 58190.v do not have complex multiplication.Modular form 58190.2.a.v
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.
\(\left(\begin{array}{rr} 1 & 5 \\ 5 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.