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Properties

Label 227850.l
Number of curves $4$
Conductor $227850$
CM no
Rank $0$
Graph

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

Elliptic curves in class 227850.l

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
227850.l1 227850ip4 \([1, 1, 0, -243041250, -1458472537500]\) \(863685084022485007249/89317200\) \(164188738481250000\) \([2]\) \(28311552\) \(3.1771\)  
227850.l2 227850ip2 \([1, 1, 0, -15191250, -22789687500]\) \(210909442362223249/67808160000\) \(124649409622500000000\) \([2, 2]\) \(14155776\) \(2.8305\)  
227850.l3 227850ip3 \([1, 1, 0, -13133250, -29183893500]\) \(-136280002216368529/121212131250000\) \(-222820094209863281250000\) \([2]\) \(28311552\) \(3.1771\)  
227850.l4 227850ip1 \([1, 1, 0, -1079250, -252823500]\) \(75627935783569/28798156800\) \(52938661708800000000\) \([2]\) \(7077888\) \(2.4840\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 227850.l have rank \(0\).

Complex multiplication

The elliptic curves in class 227850.l do not have complex multiplication.

Modular form 227850.2.a.l

sage: E.q_eigenform(10)
 
\(q - q^{2} - q^{3} + q^{4} + q^{6} - q^{8} + q^{9} - 4 q^{11} - q^{12} + 2 q^{13} + q^{16} - 2 q^{17} - q^{18} - 4 q^{19} + O(q^{20})\) 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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.