Show commands:
SageMath
E = EllipticCurve("r1")
E.isogeny_class()
Elliptic curves in class 101430.r
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
101430.r1 | 101430t2 | \([1, -1, 0, -156183750, -751241073164]\) | \(-11795263402880796810182449/404296875000000\) | \(-14441888671875000000\) | \([]\) | \(10575360\) | \(3.1745\) | |
101430.r2 | 101430t1 | \([1, -1, 0, -1778310, -1197034700]\) | \(-17410957409801706289/7266093465600000\) | \(-259552124684697600000\) | \([]\) | \(3525120\) | \(2.6252\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 101430.r have rank \(1\).
Complex multiplication
The elliptic curves in class 101430.r do not have complex multiplication.Modular form 101430.2.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 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.