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SageMath
E = EllipticCurve("bg1")
E.isogeny_class()
Elliptic curves in class 11025bg
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
11025.bg2 | 11025bg1 | \([1, -1, 0, -3537, 89046]\) | \(-9317\) | \(-525317491125\) | \([]\) | \(10080\) | \(0.98729\) | \(\Gamma_0(N)\)-optimal |
11025.bg1 | 11025bg2 | \([1, -1, 0, -91764612, -338322994479]\) | \(-162677523113838677\) | \(-525317491125\) | \([]\) | \(372960\) | \(2.7927\) |
Rank
sage: E.rank()
The elliptic curves in class 11025bg have rank \(1\).
Complex multiplication
The elliptic curves in class 11025bg do not have complex multiplication.Modular form 11025.2.a.bg
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.
\(\left(\begin{array}{rr} 1 & 37 \\ 37 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.