Properties

Label 297024.m
Number of curves $4$
Conductor $297024$
CM no
Rank $2$
Graph

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

Elliptic curves in class 297024.m

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
297024.m1 297024m4 \([0, -1, 0, -210049, -36983135]\) \(15638954062612612/205211097\) \(13448714452992\) \([2]\) \(1572864\) \(1.6633\)  
297024.m2 297024m3 \([0, -1, 0, -50209, 3755329]\) \(213597982529572/31475907099\) \(2062805047640064\) \([2]\) \(1572864\) \(1.6633\)  
297024.m3 297024m2 \([0, -1, 0, -13489, -540911]\) \(16568196345808/1744649361\) \(28584335130624\) \([2, 2]\) \(786432\) \(1.3168\)  
297024.m4 297024m1 \([0, -1, 0, 1091, -42275]\) \(140119918592/822139227\) \(-841870568448\) \([2]\) \(393216\) \(0.97018\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 297024.m have rank \(2\).

Complex multiplication

The elliptic curves in class 297024.m do not have complex multiplication.

Modular form 297024.2.a.m

sage: E.q_eigenform(10)
 
\(q - q^{3} - 2 q^{5} - q^{7} + q^{9} - 4 q^{11} - q^{13} + 2 q^{15} - q^{17} - 4 q^{19} + O(q^{20})\) 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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.