Show commands:
SageMath
E = EllipticCurve("w1")
E.isogeny_class()
Elliptic curves in class 336675w
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
336675.w2 | 336675w1 | \([0, 1, 1, 26784367, -8098792981]\) | \(1503484706816/890163675\) | \(-1258168217282992360546875\) | \([]\) | \(51701760\) | \(3.3137\) | \(\Gamma_0(N)\)-optimal |
336675.w1 | 336675w2 | \([0, 1, 1, -336824633, 2627930103644]\) | \(-2989967081734144/380653171875\) | \(-538019845239231129638671875\) | \([]\) | \(155105280\) | \(3.8630\) |
Rank
sage: E.rank()
The elliptic curves in class 336675w have rank \(1\).
Complex multiplication
The elliptic curves in class 336675w do not have complex multiplication.Modular form 336675.2.a.w
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.