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SageMath
E = EllipticCurve("bz1")
E.isogeny_class()
Elliptic curves in class 134310bz
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 134310.y2 | 134310bz1 | \([1, 0, 1, -67279, -6722278]\) | \(19010647320769/439560\) | \(778707353160\) | \([]\) | \(691200\) | \(1.3946\) | \(\Gamma_0(N)\)-optimal |
| 134310.y1 | 134310bz2 | \([1, 0, 1, -114469, 3843926]\) | \(93632326352929/50564357250\) | \(89577843294167250\) | \([]\) | \(2073600\) | \(1.9439\) |
Rank
sage: E.rank()
The elliptic curves in class 134310bz have rank \(0\).
Complex multiplication
The elliptic curves in class 134310bz do not have complex multiplication.Modular form 134310.2.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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
