Properties

Label 296450.eu
Number of curves $2$
Conductor $296450$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("eu1")
 
E.isogeny_class()
 

Elliptic curves in class 296450.eu

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
296450.eu1 296450eu2 \([1, 1, 0, -1085130, 434281940]\) \(553463785/512\) \(130722516791820800\) \([]\) \(6531840\) \(2.2074\)  
296450.eu2 296450eu1 \([1, 1, 0, -47555, -3367195]\) \(46585/8\) \(2042539324872200\) \([]\) \(2177280\) \(1.6581\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 296450.eu have rank \(0\).

Complex multiplication

The elliptic curves in class 296450.eu do not have complex multiplication.

Modular form 296450.2.a.eu

sage: E.q_eigenform(10)
 
\(q - q^{2} + 2 q^{3} + q^{4} - 2 q^{6} - q^{8} + q^{9} + 2 q^{12} + 2 q^{13} + q^{16} - 3 q^{17} - q^{18} - 8 q^{19} + O(q^{20})\) 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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.