Properties

Label 310464.hc
Number of curves $3$
Conductor $310464$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("hc1")
 
E.isogeny_class()
 

Elliptic curves in class 310464.hc

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
310464.hc1 310464hc3 \([0, 0, 0, -13795068, -19721224726]\) \(-52893159101157376/11\) \(-60379349184\) \([]\) \(4320000\) \(2.3655\)  
310464.hc2 310464hc2 \([0, 0, 0, -18228, -1715686]\) \(-122023936/161051\) \(-884014051402944\) \([]\) \(864000\) \(1.5608\)  
310464.hc3 310464hc1 \([0, 0, 0, -588, 13034]\) \(-4096/11\) \(-60379349184\) \([]\) \(172800\) \(0.75611\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 310464.hc have rank \(0\).

Complex multiplication

The elliptic curves in class 310464.hc do not have complex multiplication.

Modular form 310464.2.a.hc

sage: E.q_eigenform(10)
 
\(q - q^{5} + q^{11} + 4 q^{13} - 2 q^{17} + O(q^{20})\) 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 LMFDB numbering.

\(\left(\begin{array}{rrr} 1 & 5 & 25 \\ 5 & 1 & 5 \\ 25 & 5 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.