Properties

Label 760.d
Number of curves $2$
Conductor $760$
CM no
Rank $0$
Graph

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

Elliptic curves in class 760.d

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
760.d1 760a2 \([0, -1, 0, -20, 20]\) \(3631696/1805\) \(462080\) \([2]\) \(128\) \(-0.22008\)  
760.d2 760a1 \([0, -1, 0, 5, 0]\) \(702464/475\) \(-7600\) \([2]\) \(64\) \(-0.56666\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 760.d have rank \(0\).

Complex multiplication

The elliptic curves in class 760.d do not have complex multiplication.

Modular form 760.2.a.d

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