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SageMath
E = EllipticCurve("bd1")
E.isogeny_class()
Elliptic curves in class 323400.bd
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
323400.bd1 | 323400bd2 | \([0, -1, 0, -549208, 155622412]\) | \(4866277250/43659\) | \(164366006112000000\) | \([2]\) | \(5308416\) | \(2.1262\) | |
323400.bd2 | 323400bd1 | \([0, -1, 0, -10208, 5780412]\) | \(-62500/7623\) | \(-14349413232000000\) | \([2]\) | \(2654208\) | \(1.7797\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 323400.bd have rank \(2\).
Complex multiplication
The elliptic curves in class 323400.bd do not have complex multiplication.Modular form 323400.2.a.bd
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.