Properties

Label 1624.d
Number of curves $2$
Conductor $1624$
CM no
Rank $0$
Graph

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

Elliptic curves in class 1624.d

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
1624.d1 1624b2 \([0, -1, 0, -35768, 2615564]\) \(2471097448795250/98942809\) \(202634872832\) \([2]\) \(3072\) \(1.2525\)  
1624.d2 1624b1 \([0, -1, 0, -2128, 45468]\) \(-1041220466500/242597383\) \(-248419720192\) \([2]\) \(1536\) \(0.90590\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 1624.d have rank \(0\).

Complex multiplication

The elliptic curves in class 1624.d do not have complex multiplication.

Modular form 1624.2.a.d

sage: E.q_eigenform(10)
 
\(q + 2 q^{3} + q^{7} + q^{9} + 4 q^{13} + 2 q^{17} + 6 q^{19} + O(q^{20})\) 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.