Properties

Label 298816.z
Number of curves $2$
Conductor $298816$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("z1")
 
E.isogeny_class()
 

Elliptic curves in class 298816.z

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
298816.z1 298816z2 \([0, 0, 0, -52819276, 147753160560]\) \(62167173500157644301993/7582456\) \(1987695345664\) \([2]\) \(10616832\) \(2.6939\)  
298816.z2 298816z1 \([0, 0, 0, -3301196, 2308655984]\) \(-15177411906818559273/167619938752\) \(-43940561224204288\) \([2]\) \(5308416\) \(2.3473\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 298816.z have rank \(0\).

Complex multiplication

The elliptic curves in class 298816.z do not have complex multiplication.

Modular form 298816.2.a.z

sage: E.q_eigenform(10)
 
\(q - 2 q^{5} + q^{7} - 3 q^{9} - 4 q^{11} + 4 q^{13} + 6 q^{19} + O(q^{20})\) 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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.