Show commands:
SageMath
E = EllipticCurve("s1")
E.isogeny_class()
Elliptic curves in class 59976s
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
59976.i4 | 59976s1 | \([0, 0, 0, -311630151, 2137094698970]\) | \(-152435594466395827792/1646846627220711\) | \(-36158373657255268692999936\) | \([2]\) | \(13271040\) | \(3.7201\) | \(\Gamma_0(N)\)-optimal |
59976.i3 | 59976s2 | \([0, 0, 0, -4998939771, 136039468613510]\) | \(157304700372188331121828/18069292138401\) | \(1586926690228683686421504\) | \([2, 2]\) | \(26542080\) | \(4.0667\) | |
59976.i2 | 59976s3 | \([0, 0, 0, -5011799331, 135304372441406]\) | \(79260902459030376659234/842751810121431609\) | \(148028526018239955088831875072\) | \([2]\) | \(53084160\) | \(4.4133\) | |
59976.i1 | 59976s4 | \([0, 0, 0, -79983034131, 8706526495316174]\) | \(322159999717985454060440834/4250799\) | \(746648660747630592\) | \([2]\) | \(53084160\) | \(4.4133\) |
Rank
sage: E.rank()
The elliptic curves in class 59976s have rank \(0\).
Complex multiplication
The elliptic curves in class 59976s do not have complex multiplication.Modular form 59976.2.a.s
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 Cremona numbering.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.