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SageMath
E = EllipticCurve("bi1")
E.isogeny_class()
Elliptic curves in class 238050.bi
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
238050.bi1 | 238050bi2 | \([1, -1, 0, -13868892, -19876275824]\) | \(109348914285625/1472\) | \(3971388401380800\) | \([]\) | \(5474304\) | \(2.5501\) | |
238050.bi2 | 238050bi1 | \([1, -1, 0, -181017, -23929439]\) | \(243135625/48668\) | \(131304029020652700\) | \([]\) | \(1824768\) | \(2.0008\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 238050.bi have rank \(1\).
Complex multiplication
The elliptic curves in class 238050.bi do not have complex multiplication.Modular form 238050.2.a.bi
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.