Properties

Label 64400g
Number of curves $4$
Conductor $64400$
CM no
Rank $0$
Graph

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Show commands: SageMath
sage: E = EllipticCurve("g1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 64400g

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
64400.be4 64400g1 \([0, 0, 0, 550, -11625]\) \(73598976/276115\) \(-69028750000\) \([2]\) \(30720\) \(0.76264\) \(\Gamma_0(N)\)-optimal
64400.be3 64400g2 \([0, 0, 0, -5575, -140250]\) \(4790692944/648025\) \(2592100000000\) \([2, 2]\) \(61440\) \(1.1092\)  
64400.be2 64400g3 \([0, 0, 0, -23075, 1207250]\) \(84923690436/9794435\) \(156710960000000\) \([4]\) \(122880\) \(1.4558\)  
64400.be1 64400g4 \([0, 0, 0, -86075, -9719750]\) \(4407931365156/100625\) \(1610000000000\) \([2]\) \(122880\) \(1.4558\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 64400.2.a.g

sage: E.q_eigenform(10)
 
\(q - q^{7} - 3q^{9} - 2q^{13} + 2q^{17} - 4q^{19} + O(q^{20})\)  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.

\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.