Show commands:
SageMath
E = EllipticCurve("y1")
E.isogeny_class()
Elliptic curves in class 21780.y
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
21780.y1 | 21780w1 | \([0, 0, 0, -115797, -15797639]\) | \(-68679424/3375\) | \(-8438451709446000\) | \([]\) | \(114048\) | \(1.8175\) | \(\Gamma_0(N)\)-optimal |
21780.y2 | 21780w2 | \([0, 0, 0, 602943, -37934831]\) | \(9695350016/5859375\) | \(-14650089773343750000\) | \([3]\) | \(342144\) | \(2.3668\) |
Rank
sage: E.rank()
The elliptic curves in class 21780.y have rank \(1\).
Complex multiplication
The elliptic curves in class 21780.y do not have complex multiplication.Modular form 21780.2.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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.