Properties

Label 152460l
Number of curves $4$
Conductor $152460$
CM no
Rank $1$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("l1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 152460l

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
152460.bc3 152460l1 \([0, 0, 0, -2898192, 1927196161]\) \(-130287139815424/2250652635\) \(-46506332599167173040\) \([2]\) \(4976640\) \(2.5718\) \(\Gamma_0(N)\)-optimal
152460.bc2 152460l2 \([0, 0, 0, -46561647, 122289876214]\) \(33766427105425744/9823275\) \(3247729923373689600\) \([2]\) \(9953280\) \(2.9184\)  
152460.bc4 152460l3 \([0, 0, 0, 11215248, 9235488229]\) \(7549996227362816/6152409907875\) \(-127130245250860853694000\) \([2]\) \(14929920\) \(3.1211\)  
152460.bc1 152460l4 \([0, 0, 0, -54010407, 80553219406]\) \(52702650535889104/22020583921875\) \(7280352971207157996000000\) \([2]\) \(29859840\) \(3.4677\)  

Rank

sage: E.rank()
 

The elliptic curves in class 152460l have rank \(1\).

Complex multiplication

The elliptic curves in class 152460l do not have complex multiplication.

Modular form 152460.2.a.l

sage: E.q_eigenform(10)
 
\(q + q^{5} - q^{7} - 2q^{13} - 6q^{17} - 8q^{19} + O(q^{20})\)  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.

\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.