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SageMath
E = EllipticCurve("bi1")
E.isogeny_class()
Elliptic curves in class 380926.bi
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
380926.bi1 | 380926bi2 | \([1, 0, 0, -5014318, -4046512380]\) | \(24553362849625/1755162752\) | \(996702959188463176832\) | \([2]\) | \(25288704\) | \(2.7762\) | |
380926.bi2 | 380926bi1 | \([1, 0, 0, 285522, -276206204]\) | \(4533086375/60669952\) | \(-34452600263603372032\) | \([2]\) | \(12644352\) | \(2.4296\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 380926.bi have rank \(1\).
Complex multiplication
The elliptic curves in class 380926.bi do not have complex multiplication.Modular form 380926.2.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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.