Properties

Label 187200.bc
Number of curves $2$
Conductor $187200$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("bc1")
 
E.isogeny_class()
 

Elliptic curves in class 187200.bc

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
187200.bc1 187200co2 \([0, 0, 0, -1937100, -1037872240]\) \(-168256703745625/30371328\) \(-145101279146803200\) \([]\) \(2985984\) \(2.2967\)  
187200.bc2 187200co1 \([0, 0, 0, 6900, -4752880]\) \(7604375/2047032\) \(-9779847679180800\) \([]\) \(995328\) \(1.7474\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 187200.bc have rank \(0\).

Complex multiplication

The elliptic curves in class 187200.bc do not have complex multiplication.

Modular form 187200.2.a.bc

sage: E.q_eigenform(10)
 
\(q - 4 q^{7} + q^{13} + 5 q^{19} + O(q^{20})\) 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.

\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.