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SageMath
E = EllipticCurve("bv1")
E.isogeny_class()
Elliptic curves in class 127050bv
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
127050.h1 | 127050bv1 | \([1, 1, 0, -515825, -142042875]\) | \(4386781853/27216\) | \(94169539406250000\) | \([2]\) | \(2240000\) | \(2.0950\) | \(\Gamma_0(N)\)-optimal |
127050.h2 | 127050bv2 | \([1, 1, 0, -213325, -306905375]\) | \(-310288733/11573604\) | \(-40045596632507812500\) | \([2]\) | \(4480000\) | \(2.4416\) |
Rank
sage: E.rank()
The elliptic curves in class 127050bv have rank \(1\).
Complex multiplication
The elliptic curves in class 127050bv do not have complex multiplication.Modular form 127050.2.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 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.