Show commands:
SageMath
E = EllipticCurve("q1")
E.isogeny_class()
Elliptic curves in class 256025.q
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
256025.q1 | 256025q1 | \([0, 1, 1, -33483, -2769056]\) | \(-2258403328/480491\) | \(-883270088421875\) | \([]\) | \(746496\) | \(1.5893\) | \(\Gamma_0(N)\)-optimal |
256025.q2 | 256025q2 | \([0, 1, 1, 236017, 16028569]\) | \(790939860992/517504691\) | \(-951311084241546875\) | \([]\) | \(2239488\) | \(2.1386\) |
Rank
sage: E.rank()
The elliptic curves in class 256025.q have rank \(1\).
Complex multiplication
The elliptic curves in class 256025.q do not have complex multiplication.Modular form 256025.2.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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.