Properties

Label 154128ca
Number of curves $4$
Conductor $154128$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("ca1")
 
E.isogeny_class()
 

Elliptic curves in class 154128ca

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
154128.bk3 154128ca1 \([0, -1, 0, -4112, 89088]\) \(389017/57\) \(1126924750848\) \([2]\) \(184320\) \(1.0375\) \(\Gamma_0(N)\)-optimal
154128.bk2 154128ca2 \([0, -1, 0, -17632, -808640]\) \(30664297/3249\) \(64234710798336\) \([2, 2]\) \(368640\) \(1.3840\)  
154128.bk4 154128ca3 \([0, -1, 0, 22928, -4020992]\) \(67419143/390963\) \(-7729576866066432\) \([2]\) \(737280\) \(1.7306\)  
154128.bk1 154128ca4 \([0, -1, 0, -274512, -55267200]\) \(115714886617/1539\) \(30426968272896\) \([2]\) \(737280\) \(1.7306\)  

Rank

sage: E.rank()
 

The elliptic curves in class 154128ca have rank \(0\).

Complex multiplication

The elliptic curves in class 154128ca do not have complex multiplication.

Modular form 154128.2.a.ca

sage: E.q_eigenform(10)
 
\(q - q^{3} + 2 q^{5} + q^{9} - 2 q^{15} - 6 q^{17} - q^{19} + O(q^{20})\) 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 Cremona 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 Cremona labels.