Properties

Label 29760cb
Number of curves $2$
Conductor $29760$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("cb1")
 
E.isogeny_class()
 

Elliptic curves in class 29760cb

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
29760.bi2 29760cb1 \([0, -1, 0, -2625, 53985]\) \(-7633736209/230640\) \(-60460892160\) \([2]\) \(30720\) \(0.84657\) \(\Gamma_0(N)\)-optimal
29760.bi1 29760cb2 \([0, -1, 0, -42305, 3363297]\) \(31942518433489/27900\) \(7313817600\) \([2]\) \(61440\) \(1.1931\)  

Rank

sage: E.rank()
 

The elliptic curves in class 29760cb have rank \(0\).

Complex multiplication

The elliptic curves in class 29760cb do not have complex multiplication.

Modular form 29760.2.a.cb

sage: E.q_eigenform(10)
 
\(q - q^{3} + q^{5} + 2 q^{7} + q^{9} - 4 q^{13} - q^{15} + 6 q^{17} + O(q^{20})\) Copy content Toggle raw display

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.

\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)

Isogeny graph

sage: E.isogeny_graph().plot(edge_labels=True)
 

The vertices are labelled with Cremona labels.