Show commands:
SageMath
E = EllipticCurve("q1")
E.isogeny_class()
Elliptic curves in class 148225.q
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
148225.q1 | 148225t2 | \([1, 1, 1, -30843105763, -2084913037989594]\) | \(-162677523113838677\) | \(-19946673094455078125\) | \([]\) | \(89510400\) | \(4.2471\) | |
148225.q2 | 148225t1 | \([1, 1, 1, -1188888, 542760406]\) | \(-9317\) | \(-19946673094455078125\) | \([]\) | \(2419200\) | \(2.4416\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 148225.q have rank \(1\).
Complex multiplication
The elliptic curves in class 148225.q do not have complex multiplication.Modular form 148225.2.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.
\(\left(\begin{array}{rr} 1 & 37 \\ 37 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.