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SageMath
E = EllipticCurve("bz1")
E.isogeny_class()
Elliptic curves in class 68544bz
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 68544.bj2 | 68544bz1 | \([0, 0, 0, -12396, -745040]\) | \(-1102302937/616896\) | \(-117890661482496\) | \([2]\) | \(147456\) | \(1.4034\) | \(\Gamma_0(N)\)-optimal |
| 68544.bj1 | 68544bz2 | \([0, 0, 0, -219756, -39645776]\) | \(6141556990297/1019592\) | \(194847065505792\) | \([2]\) | \(294912\) | \(1.7499\) |
Rank
sage: E.rank()
The elliptic curves in class 68544bz have rank \(1\).
Complex multiplication
The elliptic curves in class 68544bz do not have complex multiplication.Modular form 68544.2.a.bz
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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
