Show commands:
SageMath
E = EllipticCurve("q1")
E.isogeny_class()
Elliptic curves in class 257754q
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
257754.q2 | 257754q1 | \([1, 1, 0, 371424, -22514688]\) | \(15697286016456868703/9699053927399424\) | \(-3501358467791192064\) | \([]\) | \(5878656\) | \(2.2474\) | \(\Gamma_0(N)\)-optimal |
257754.q1 | 257754q2 | \([1, 1, 0, -4443936, 4091116032]\) | \(-26885619637842619882657/4488366981249252864\) | \(-1620300480230980283904\) | \([]\) | \(17635968\) | \(2.7967\) |
Rank
sage: E.rank()
The elliptic curves in class 257754q have rank \(1\).
Complex multiplication
The elliptic curves in class 257754q do not have complex multiplication.Modular form 257754.2.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 Cremona 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 Cremona labels.