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SageMath
E = EllipticCurve("br1")
E.isogeny_class()
Elliptic curves in class 22800.br
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
22800.br1 | 22800bv4 | \([0, -1, 0, -196992008, -1064128873488]\) | \(13209596798923694545921/92340\) | \(5909760000000\) | \([2]\) | \(2211840\) | \(2.9854\) | |
22800.br2 | 22800bv3 | \([0, -1, 0, -12464008, -16192233488]\) | \(3345930611358906241/165622259047500\) | \(10599824579040000000000\) | \([2]\) | \(2211840\) | \(2.9854\) | |
22800.br3 | 22800bv2 | \([0, -1, 0, -12312008, -16623913488]\) | \(3225005357698077121/8526675600\) | \(545707238400000000\) | \([2, 2]\) | \(1105920\) | \(2.6388\) | |
22800.br4 | 22800bv1 | \([0, -1, 0, -760008, -266281488]\) | \(-758575480593601/40535043840\) | \(-2594242805760000000\) | \([2]\) | \(552960\) | \(2.2922\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 22800.br have rank \(0\).
Complex multiplication
The elliptic curves in class 22800.br do not have complex multiplication.Modular form 22800.2.a.br
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.
\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.