Properties

Label 92400cm
Number of curves $6$
Conductor $92400$
CM no
Rank $0$
Graph

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Show commands: SageMath
sage: E = EllipticCurve("cm1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 92400cm

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
92400.ic5 92400cm1 \([0, 1, 0, 57617, -17512012]\) \(84611246065664/580054565475\) \(-145013641368750000\) \([2]\) \(786432\) \(1.9746\) \(\Gamma_0(N)\)-optimal
92400.ic4 92400cm2 \([0, 1, 0, -762508, -234025012]\) \(12257375872392016/1191317675625\) \(4765270702500000000\) \([2, 2]\) \(1572864\) \(2.3212\)  
92400.ic3 92400cm3 \([0, 1, 0, -2747008, 1492489988]\) \(143279368983686884/22699269140625\) \(363188306250000000000\) \([2, 2]\) \(3145728\) \(2.6678\)  
92400.ic2 92400cm4 \([0, 1, 0, -11900008, -15804250012]\) \(11647843478225136004/128410942275\) \(2054575076400000000\) \([2]\) \(3145728\) \(2.6678\)  
92400.ic6 92400cm5 \([0, 1, 0, 4875992, 8307451988]\) \(400647648358480318/1163177490234375\) \(-37221679687500000000000\) \([2]\) \(6291456\) \(3.0144\)  
92400.ic1 92400cm6 \([0, 1, 0, -42122008, 105206239988]\) \(258286045443018193442/8440380939375\) \(270092190060000000000\) \([2]\) \(6291456\) \(3.0144\)  

Rank

sage: E.rank()
 

The elliptic curves in class 92400cm have rank \(0\).

Complex multiplication

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

Modular form 92400.2.a.cm

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

\(\left(\begin{array}{rrrrrr} 1 & 2 & 4 & 4 & 8 & 8 \\ 2 & 1 & 2 & 2 & 4 & 4 \\ 4 & 2 & 1 & 4 & 2 & 2 \\ 4 & 2 & 4 & 1 & 8 & 8 \\ 8 & 4 & 2 & 8 & 1 & 4 \\ 8 & 4 & 2 & 8 & 4 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.