Properties

Label 4410.d
Number of curves $2$
Conductor $4410$
CM no
Rank $0$
Graph

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

Elliptic curves in class 4410.d

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
4410.d1 4410a2 \([1, -1, 0, -87915, -10011275]\) \(68971442301/400\) \(435818955600\) \([2]\) \(14336\) \(1.4236\)  
4410.d2 4410a1 \([1, -1, 0, -5595, -149339]\) \(17779581/1280\) \(1394620657920\) \([2]\) \(7168\) \(1.0770\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 4410.d have rank \(0\).

Complex multiplication

The elliptic curves in class 4410.d do not have complex multiplication.

Modular form 4410.2.a.d

sage: E.q_eigenform(10)
 
\(q - q^{2} + q^{4} - q^{5} - q^{8} + q^{10} - 2 q^{11} + 2 q^{13} + q^{16} - 2 q^{17} + 6 q^{19} + O(q^{20})\) 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.