Show commands:
SageMath
E = EllipticCurve("q1")
E.isogeny_class()
Elliptic curves in class 190440.q
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
190440.q1 | 190440v2 | \([0, 0, 0, -712563, -224043138]\) | \(9776035692/359375\) | \(1470884593104000000\) | \([2]\) | \(2433024\) | \(2.2554\) | |
190440.q2 | 190440v1 | \([0, 0, 0, 17457, -12483342]\) | \(574992/66125\) | \(-67660691282784000\) | \([2]\) | \(1216512\) | \(1.9088\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 190440.q have rank \(1\).
Complex multiplication
The elliptic curves in class 190440.q do not have complex multiplication.Modular form 190440.2.a.q
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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.