Properties

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

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Show commands: SageMath
sage: E = EllipticCurve("m1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 64400.m

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
64400.m1 64400ca4 \([0, 1, 0, -66732408, 209800175188]\) \(513516182162686336369/1944885031250\) \(124472642000000000000\) \([2]\) \(8626176\) \(3.0705\)  
64400.m2 64400ca3 \([0, 1, 0, -4232408, 3175175188]\) \(131010595463836369/7704101562500\) \(493062500000000000000\) \([2]\) \(4313088\) \(2.7239\)  
64400.m3 64400ca2 \([0, 1, 0, -1136408, 49559188]\) \(2535986675931409/1450751712200\) \(92848109580800000000\) \([2]\) \(2875392\) \(2.5212\)  
64400.m4 64400ca1 \([0, 1, 0, -736408, -242440812]\) \(690080604747409/3406760000\) \(218032640000000000\) \([2]\) \(1437696\) \(2.1746\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 64400.2.a.m

sage: E.q_eigenform(10)
 
\(q - 2q^{3} + q^{7} + q^{9} + 6q^{11} + 4q^{13} - 6q^{17} - 8q^{19} + O(q^{20})\)  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 LMFDB numbering.

\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.