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Properties

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

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Show commands: SageMath
E = EllipticCurve("cd1")
 
E.isogeny_class()
 

Elliptic curves in class 298816.cd

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
298816.cd1 298816cd2 \([0, -1, 0, -11079113057, -448850814066175]\) \(573718392227901342193352375257/22016176259779893044\) \(5771408509443740282126336\) \([2]\) \(279379968\) \(4.2423\)  
298816.cd2 298816cd1 \([0, -1, 0, -691415137, -7035013513983]\) \(-139444195316122186685933977/867810592237096964848\) \(-227491339891401546753114112\) \([2]\) \(139689984\) \(3.8957\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 298816.2.a.cd

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