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Properties

Label 237910.d
Number of curves $2$
Conductor $237910$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("d1")
 
E.isogeny_class()
 

Elliptic curves in class 237910.d

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
237910.d1 237910d2 \([1, -1, 1, -2142938068797, -1207431080854081371]\) \(1088309881108300742016838020617212688383521/269028640626960381689440\) \(269028640626960381689440\) \([]\) \(3779805120\) \(5.2684\)  
237910.d2 237910d1 \([1, -1, 1, -1372533597, 1939871690469]\) \(285951687415542722080196235890721/163856215505464081776640000000\) \(163856215505464081776640000000\) \([7]\) \(539972160\) \(4.2954\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 237910.d have rank \(0\).

Complex multiplication

The elliptic curves in class 237910.d do not have complex multiplication.

Modular form 237910.2.a.d

sage: E.q_eigenform(10)
 
\(q + q^{2} - 3 q^{3} + q^{4} + q^{5} - 3 q^{6} + q^{7} + q^{8} + 6 q^{9} + q^{10} - 2 q^{11} - 3 q^{12} + 7 q^{13} + q^{14} - 3 q^{15} + q^{16} + 4 q^{17} + 6 q^{18} - q^{19} + O(q^{20})\) 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.

\(\left(\begin{array}{rr} 1 & 7 \\ 7 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.