Show commands:
SageMath
E = EllipticCurve("z1")
E.isogeny_class()
Elliptic curves in class 270480z
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
270480.z1 | 270480z1 | \([0, -1, 0, -10061, -156624]\) | \(174456832/83835\) | \(54128714285520\) | \([2]\) | \(645120\) | \(1.3289\) | \(\Gamma_0(N)\)-optimal |
270480.z2 | 270480z2 | \([0, -1, 0, 36244, -1230900]\) | \(509680208/357075\) | \(-3688771640198400\) | \([2]\) | \(1290240\) | \(1.6755\) |
Rank
sage: E.rank()
The elliptic curves in class 270480z have rank \(0\).
Complex multiplication
The elliptic curves in class 270480z do not have complex multiplication.Modular form 270480.2.a.z
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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.