Properties

Label 1596.d
Number of curves $2$
Conductor $1596$
CM no
Rank $1$
Graph

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

Elliptic curves in class 1596.d

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
1596.d1 1596e2 \([0, 1, 0, -4884, 129636]\) \(50338425969232/54974619\) \(14073502464\) \([2]\) \(1920\) \(0.86258\)  
1596.d2 1596e1 \([0, 1, 0, -229, 3020]\) \(-83369132032/210622923\) \(-3369966768\) \([2]\) \(960\) \(0.51600\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 1596.d have rank \(1\).

Complex multiplication

The elliptic curves in class 1596.d do not have complex multiplication.

Modular form 1596.2.a.d

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