Properties

Label 624.d
Number of curves $4$
Conductor $624$
CM no
Rank $0$
Graph

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

Elliptic curves in class 624.d

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
624.d1 624c3 \([0, -1, 0, -832, 9520]\) \(62275269892/39\) \(39936\) \([2]\) \(128\) \(0.20313\)  
624.d2 624c2 \([0, -1, 0, -52, 160]\) \(61918288/1521\) \(389376\) \([2, 2]\) \(64\) \(-0.14345\)  
624.d3 624c1 \([0, -1, 0, -7, -2]\) \(2725888/1053\) \(16848\) \([2]\) \(32\) \(-0.49002\) \(\Gamma_0(N)\)-optimal
624.d4 624c4 \([0, -1, 0, 8, 448]\) \(48668/85683\) \(-87739392\) \([4]\) \(128\) \(0.20313\)  

Rank

sage: E.rank()
 

The elliptic curves in class 624.d have rank \(0\).

Complex multiplication

The elliptic curves in class 624.d do not have complex multiplication.

Modular form 624.2.a.d

sage: E.q_eigenform(10)
 
\(q - q^{3} + 2 q^{5} + q^{9} + q^{13} - 2 q^{15} + 2 q^{17} + 4 q^{19} + O(q^{20})\) 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.

\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.