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Properties

Label 185150.bs
Number of curves $2$
Conductor $185150$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("bs1")
 
E.isogeny_class()
 

Elliptic curves in class 185150.bs

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
185150.bs1 185150t2 \([1, -1, 1, -206444730, 1141624235897]\) \(420676324562824569/56350000000\) \(130340974142968750000000\) \([2]\) \(34062336\) \(3.4544\)  
185150.bs2 185150t1 \([1, -1, 1, -11772730, 21092203897]\) \(-78013216986489/37918720000\) \(-87708303514720000000000\) \([2]\) \(17031168\) \(3.1078\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 185150.bs have rank \(1\).

Complex multiplication

The elliptic curves in class 185150.bs do not have complex multiplication.

Modular form 185150.2.a.bs

sage: E.q_eigenform(10)
 
\(q + q^{2} + q^{4} - q^{7} + q^{8} - 3 q^{9} - 4 q^{13} - q^{14} + q^{16} + 4 q^{17} - 3 q^{18} + 2 q^{19} + O(q^{20})\) 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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.