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SageMath
E = EllipticCurve("bh1")
E.isogeny_class()
Elliptic curves in class 129360.bh
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 129360.bh1 | 129360be2 | \([0, -1, 0, -17395016, -26360897520]\) | \(7043457887336414/442092481875\) | \(36536373803496188160000\) | \([2]\) | \(11354112\) | \(3.0806\) | |
| 129360.bh2 | 129360be1 | \([0, -1, 0, 866304, -1730029104]\) | \(1740010436132/32286699225\) | \(-1334154006377323084800\) | \([2]\) | \(5677056\) | \(2.7340\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 129360.bh have rank \(1\).
Complex multiplication
The elliptic curves in class 129360.bh do not have complex multiplication.Modular form 129360.2.a.bh
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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
