Show commands:
SageMath
E = EllipticCurve("m1")
E.isogeny_class()
Elliptic curves in class 6042.m
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
6042.m1 | 6042m2 | \([1, 0, 0, -107, 345]\) | \(135559106353/24337176\) | \(24337176\) | \([2]\) | \(2304\) | \(0.13641\) | |
6042.m2 | 6042m1 | \([1, 0, 0, 13, 33]\) | \(241804367/580032\) | \(-580032\) | \([2]\) | \(1152\) | \(-0.21016\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 6042.m have rank \(0\).
Complex multiplication
The elliptic curves in class 6042.m do not have complex multiplication.Modular form 6042.2.a.m
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.