Properties

Label 154800bw
Number of curves $2$
Conductor $154800$
CM no
Rank $1$
Graph

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Show commands: SageMath
sage: E = EllipticCurve("bw1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 154800bw

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
154800.br2 154800bw1 \([0, 0, 0, -135075, 12825250]\) \(5841725401/1857600\) \(86668185600000000\) \([2]\) \(1327104\) \(1.9539\) \(\Gamma_0(N)\)-optimal
154800.br1 154800bw2 \([0, 0, 0, -855075, -294614750]\) \(1481933914201/53916840\) \(2515544087040000000\) \([2]\) \(2654208\) \(2.3005\)  

Rank

sage: E.rank()
 

The elliptic curves in class 154800bw have rank \(1\).

Complex multiplication

The elliptic curves in class 154800bw do not have complex multiplication.

Modular form 154800.2.a.bw

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

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

Isogeny graph

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

The vertices are labelled with Cremona labels.