Properties

Label 58800.kc
Number of curves $2$
Conductor $58800$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("kc1")
 
E.isogeny_class()
 

Elliptic curves in class 58800.kc

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
58800.kc1 58800jd2 \([0, 1, 0, -37508, 1756488]\) \(4253563312/1476225\) \(2025380700000000\) \([2]\) \(368640\) \(1.6387\)  
58800.kc2 58800jd1 \([0, 1, 0, -15633, -737262]\) \(4927700992/151875\) \(13023281250000\) \([2]\) \(184320\) \(1.2921\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 58800.kc have rank \(0\).

Complex multiplication

The elliptic curves in class 58800.kc do not have complex multiplication.

Modular form 58800.2.a.kc

sage: E.q_eigenform(10)
 
\(q + q^{3} + q^{9} + 6 q^{11} + 6 q^{17} + 4 q^{19} + O(q^{20})\) 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 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.