Show commands:
SageMath
E = EllipticCurve("y1")
E.isogeny_class()
Elliptic curves in class 20160.y
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
20160.y1 | 20160cs4 | \([0, 0, 0, -15228, 289872]\) | \(1210991472/588245\) | \(189700937072640\) | \([2]\) | \(55296\) | \(1.4332\) | |
20160.y2 | 20160cs3 | \([0, 0, 0, -12528, 539352]\) | \(10788913152/8575\) | \(172832486400\) | \([2]\) | \(27648\) | \(1.0866\) | |
20160.y3 | 20160cs2 | \([0, 0, 0, -8028, -276848]\) | \(129348709488/6125\) | \(2709504000\) | \([2]\) | \(18432\) | \(0.88389\) | |
20160.y4 | 20160cs1 | \([0, 0, 0, -528, -3848]\) | \(588791808/109375\) | \(3024000000\) | \([2]\) | \(9216\) | \(0.53732\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 20160.y have rank \(0\).
Complex multiplication
The elliptic curves in class 20160.y do not have complex multiplication.Modular form 20160.2.a.y
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.