Properties

Label 64400.h
Number of curves $2$
Conductor $64400$
CM no
Rank $0$
Graph

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Show commands: SageMath
sage: E = EllipticCurve("h1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 64400.h

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
64400.h1 64400ci2 \([0, 1, 0, -148, 408]\) \(11279504/3703\) \(118496000\) \([2]\) \(23040\) \(0.25222\)  
64400.h2 64400ci1 \([0, 1, 0, 27, 58]\) \(1048576/1127\) \(-2254000\) \([2]\) \(11520\) \(-0.094350\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 64400.h have rank \(0\).

Complex multiplication

The elliptic curves in class 64400.h do not have complex multiplication.

Modular form 64400.2.a.h

sage: E.q_eigenform(10)
 
\(q - 2q^{3} + q^{7} + q^{9} - 2q^{11} + 6q^{13} + 6q^{17} + O(q^{20})\)  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.