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SageMath
E = EllipticCurve("bo1")
E.isogeny_class()
Elliptic curves in class 72128bo
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 72128.h2 | 72128bo1 | \([0, 1, 0, -13729, -625185]\) | \(-3183010111/8464\) | \(-761043877888\) | \([2]\) | \(98304\) | \(1.1546\) | \(\Gamma_0(N)\)-optimal |
| 72128.h1 | 72128bo2 | \([0, 1, 0, -219809, -39739169]\) | \(13062552753151/92\) | \(8272216064\) | \([2]\) | \(196608\) | \(1.5012\) |
Rank
sage: E.rank()
The elliptic curves in class 72128bo have rank \(1\).
Complex multiplication
The elliptic curves in class 72128bo do not have complex multiplication.Modular form 72128.2.a.bo
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.
