Show commands:
SageMath
E = EllipticCurve("a1")
E.isogeny_class()
Elliptic curves in class 672.a
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
672.a1 | 672d2 | \([0, -1, 0, -1505, -17199]\) | \(92100460096/20253807\) | \(82959593472\) | \([2]\) | \(960\) | \(0.80865\) | |
672.a2 | 672d1 | \([0, -1, 0, 210, -1764]\) | \(15926924096/28588707\) | \(-1829677248\) | \([2]\) | \(480\) | \(0.46208\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 672.a have rank \(0\).
Complex multiplication
The elliptic curves in class 672.a do not have complex multiplication.Modular form 672.2.a.a
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.