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SageMath
E = EllipticCurve("bv1")
E.isogeny_class()
Elliptic curves in class 64400.bv
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 64400.bv1 | 64400bp2 | \([0, 1, 0, -416852248, 3295522252948]\) | \(-78229436189152112196207745/549794097750525813248\) | \(-56298915609653843276595200\) | \([]\) | \(15676416\) | \(3.7743\) | |
| 64400.bv2 | 64400bp1 | \([0, 1, 0, 14661352, 24099235988]\) | \(3403656999841015798655/4418852112356605952\) | \(-452490456305316449484800\) | \([]\) | \(5225472\) | \(3.2250\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 64400.bv have rank \(1\).
Complex multiplication
The elliptic curves in class 64400.bv do not have complex multiplication.Modular form 64400.2.a.bv
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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
