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SageMath
E = EllipticCurve("bd1")
E.isogeny_class()
Elliptic curves in class 92910.bd
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
92910.bd1 | 92910bi3 | \([1, 0, 0, -101809080, -441623441058]\) | \(-116703330783653990330906728321/16713618975051084640111710\) | \(-16713618975051084640111710\) | \([]\) | \(30548016\) | \(3.5706\) | |
92910.bd2 | 92910bi1 | \([1, 0, 0, -1577130, 794918052]\) | \(-433836620224795849583521/22005928611000000000\) | \(-22005928611000000000\) | \([9]\) | \(3394224\) | \(2.4720\) | \(\Gamma_0(N)\)-optimal |
92910.bd3 | 92910bi2 | \([1, 0, 0, 8277870, 1819757052]\) | \(62730610483865150939136479/37731927035519394651000\) | \(-37731927035519394651000\) | \([3]\) | \(10182672\) | \(3.0213\) |
Rank
sage: E.rank()
The elliptic curves in class 92910.bd have rank \(0\).
Complex multiplication
The elliptic curves in class 92910.bd do not have complex multiplication.Modular form 92910.2.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.
\(\left(\begin{array}{rrr} 1 & 9 & 3 \\ 9 & 1 & 3 \\ 3 & 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.