Properties

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

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Show commands: SageMath
sage: E = EllipticCurve("ce1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 64400ce

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
64400.o2 64400ce1 \([0, -1, 0, 366533792, 3011671430912]\) \(3403656999841015798655/4418852112356605952\) \(-7070163379770569523200000000\) \([]\) \(26127360\) \(4.0297\) \(\Gamma_0(N)\)-optimal
64400.o1 64400ce2 \([0, -1, 0, -10421306208, 411961124230912]\) \(-78229436189152112196207745/549794097750525813248\) \(-879670556400841301196800000000\) \([]\) \(78382080\) \(4.5790\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 64400.2.a.ce

sage: E.q_eigenform(10)
 
\(q - q^{3} - q^{7} - 2q^{9} - 3q^{11} + 2q^{13} + 3q^{17} - 5q^{19} + O(q^{20})\)  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 Cremona numbering.

\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.