Properties

Label 360.e
Number of curves $4$
Conductor $360$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("e1")
 
E.isogeny_class()
 

Elliptic curves in class 360.e

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
360.e1 360d4 \([0, 0, 0, -1947, 33046]\) \(546718898/405\) \(604661760\) \([2]\) \(256\) \(0.61871\)  
360.e2 360d3 \([0, 0, 0, -1227, -16346]\) \(136835858/1875\) \(2799360000\) \([2]\) \(256\) \(0.61871\)  
360.e3 360d2 \([0, 0, 0, -147, 286]\) \(470596/225\) \(167961600\) \([2, 2]\) \(128\) \(0.27214\)  
360.e4 360d1 \([0, 0, 0, 33, 34]\) \(21296/15\) \(-2799360\) \([4]\) \(64\) \(-0.074438\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 360.e have rank \(0\).

Complex multiplication

The elliptic curves in class 360.e do not have complex multiplication.

Modular form 360.2.a.e

sage: E.q_eigenform(10)
 
\(q + q^{5} + 4 q^{7} - 6 q^{13} + 2 q^{17} + 4 q^{19} + O(q^{20})\) 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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.