Show commands:
SageMath
E = EllipticCurve("bq1")
E.isogeny_class()
Elliptic curves in class 64400bq
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 64400.bz1 | 64400bq1 | \([0, 1, 0, -65820258, -205557744637]\) | \(-126142795384287538429696/9315359375\) | \(-2328839843750000\) | \([]\) | \(3400704\) | \(2.8449\) | \(\Gamma_0(N)\)-optimal |
| 64400.bz2 | 64400bq2 | \([0, 1, 0, -65157758, -209897582137]\) | \(-122372013839654770813696/5297595236711512175\) | \(-1324398809177878043750000\) | \([]\) | \(10202112\) | \(3.3942\) |
Rank
sage: E.rank()
The elliptic curves in class 64400bq have rank \(1\).
Complex multiplication
The elliptic curves in class 64400bq do not have complex multiplication.Modular form 64400.2.a.bq
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.
