Properties

Label 273600.hj
Number of curves $4$
Conductor $273600$
CM no
Rank $1$
Graph

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Show commands: SageMath
sage: E = EllipticCurve("hj1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 273600.hj

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
273600.hj1 273600hj4 \([0, 0, 0, -8942700, -10278254000]\) \(26487576322129/44531250\) \(132969600000000000000\) \([2]\) \(9437184\) \(2.7567\)  
273600.hj2 273600hj2 \([0, 0, 0, -734700, -51086000]\) \(14688124849/8122500\) \(24253655040000000000\) \([2, 2]\) \(4718592\) \(2.4101\)  
273600.hj3 273600hj1 \([0, 0, 0, -446700, 114226000]\) \(3301293169/22800\) \(68080435200000000\) \([2]\) \(2359296\) \(2.0635\) \(\Gamma_0(N)\)-optimal
273600.hj4 273600hj3 \([0, 0, 0, 2865300, -403886000]\) \(871257511151/527800050\) \(-1576002504499200000000\) \([2]\) \(9437184\) \(2.7567\)  

Rank

sage: E.rank()
 

The elliptic curves in class 273600.hj have rank \(1\).

Complex multiplication

The elliptic curves in class 273600.hj do not have complex multiplication.

Modular form 273600.2.a.hj

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