Properties

Label 78400.jd
Number of curves $2$
Conductor $78400$
CM no
Rank $0$
Graph

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Show commands: SageMath
sage: E = EllipticCurve("jd1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 78400.jd

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
78400.jd1 78400cn2 \([0, -1, 0, -24033, 1027937]\) \(2185454/625\) \(439040000000000\) \([2]\) \(294912\) \(1.5162\)  
78400.jd2 78400cn1 \([0, -1, 0, 3967, 103937]\) \(19652/25\) \(-8780800000000\) \([2]\) \(147456\) \(1.1696\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 78400.jd have rank \(0\).

Complex multiplication

The elliptic curves in class 78400.jd do not have complex multiplication.

Modular form 78400.2.a.jd

sage: E.q_eigenform(10)
 
\(q + 2 q^{3} + q^{9} - 4 q^{11} + 2 q^{13} - 2 q^{19} + O(q^{20})\) 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.