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SageMath
E = EllipticCurve("bn1")
E.isogeny_class()
Elliptic curves in class 35574.bn
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
35574.bn1 | 35574cf2 | \([1, 1, 1, -4218607, -3353831755]\) | \(-16591834777/98304\) | \(-49193497519098003456\) | \([]\) | \(1701000\) | \(2.6188\) | |
35574.bn2 | 35574cf1 | \([1, 1, 1, 139208, -24461095]\) | \(596183/864\) | \(-432364724288947296\) | \([]\) | \(567000\) | \(2.0695\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 35574.bn have rank \(0\).
Complex multiplication
The elliptic curves in class 35574.bn do not have complex multiplication.Modular form 35574.2.a.bn
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.