Show commands:
SageMath
E = EllipticCurve("j1")
E.isogeny_class()
Elliptic curves in class 490.j
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
490.j1 | 490i2 | \([1, 1, 1, -24060, 1426487]\) | \(-5452947409/250\) | \(-70618812250\) | \([]\) | \(1260\) | \(1.1573\) | |
490.j2 | 490i1 | \([1, 1, 1, -50, 5095]\) | \(-49/40\) | \(-11299009960\) | \([]\) | \(420\) | \(0.60804\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 490.j have rank \(0\).
Complex multiplication
The elliptic curves in class 490.j do not have complex multiplication.Modular form 490.2.a.j
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.