Properties

Label 92400.dj
Number of curves $4$
Conductor $92400$
CM no
Rank $1$
Graph

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Show commands: SageMath
sage: E = EllipticCurve("dj1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 92400.dj

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
92400.dj1 92400w4 \([0, -1, 0, -407367408, 2803021257312]\) \(233632133015204766393938/29145526885986328125\) \(932656860351562500000000000\) \([2]\) \(47185920\) \(3.9047\)  
92400.dj2 92400w2 \([0, -1, 0, -101754408, -349682450688]\) \(7282213870869695463556/912102595400390625\) \(14593641526406250000000000\) \([2, 2]\) \(23592960\) \(3.5581\)  
92400.dj3 92400w1 \([0, -1, 0, -98473908, -376083914688]\) \(26401417552259125806544/507547744790625\) \(2030190979162500000000\) \([2]\) \(11796480\) \(3.2115\) \(\Gamma_0(N)\)-optimal
92400.dj4 92400w3 \([0, -1, 0, 151370592, -1812744950688]\) \(11986661998777424518222/51295853620928503125\) \(-1641467315869712100000000000\) \([4]\) \(47185920\) \(3.9047\)  

Rank

sage: E.rank()
 

The elliptic curves in class 92400.dj have rank \(1\).

Complex multiplication

The elliptic curves in class 92400.dj do not have complex multiplication.

Modular form 92400.2.a.dj

sage: E.q_eigenform(10)
 
\(q - q^{3} + q^{7} + q^{9} + q^{11} - 2q^{13} + 6q^{17} + 4q^{19} + O(q^{20})\)  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.