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SageMath
E = EllipticCurve("bs1")
E.isogeny_class()
Elliptic curves in class 24150bs
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
24150.ca3 | 24150bs1 | \([1, 1, 1, -8838, -323469]\) | \(4886171981209/270480\) | \(4226250000\) | \([2]\) | \(36864\) | \(0.91258\) | \(\Gamma_0(N)\)-optimal |
24150.ca2 | 24150bs2 | \([1, 1, 1, -9338, -285469]\) | \(5763259856089/1143116100\) | \(17861189062500\) | \([2, 2]\) | \(73728\) | \(1.2591\) | |
24150.ca4 | 24150bs3 | \([1, 1, 1, 19412, -1665469]\) | \(51774168853511/107398242630\) | \(-1678097541093750\) | \([2]\) | \(147456\) | \(1.6057\) | |
24150.ca1 | 24150bs4 | \([1, 1, 1, -46088, 3536531]\) | \(692895692874169/51420783750\) | \(803449746093750\) | \([2]\) | \(147456\) | \(1.6057\) |
Rank
sage: E.rank()
The elliptic curves in class 24150bs have rank \(1\).
Complex multiplication
The elliptic curves in class 24150bs do not have complex multiplication.Modular form 24150.2.a.bs
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 Cremona numbering.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.