Show commands:
SageMath
E = EllipticCurve("w1")
E.isogeny_class()
Elliptic curves in class 355740.w
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
355740.w1 | 355740w1 | \([0, -1, 0, -5210, 152517]\) | \(-68679424/3375\) | \(-768718566000\) | \([]\) | \(466560\) | \(1.0422\) | \(\Gamma_0(N)\)-optimal |
355740.w2 | 355740w2 | \([0, -1, 0, 27130, 353025]\) | \(9695350016/5859375\) | \(-1334580843750000\) | \([]\) | \(1399680\) | \(1.5915\) |
Rank
sage: E.rank()
The elliptic curves in class 355740.w have rank \(1\).
Complex multiplication
The elliptic curves in class 355740.w do not have complex multiplication.Modular form 355740.2.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 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.