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Properties

Label 43350s
Number of curves $2$
Conductor $43350$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("s1")
 
E.isogeny_class()
 

Elliptic curves in class 43350s

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
43350.q2 43350s1 \([1, 1, 0, -11137901200, 240153162784000]\) \(16206164115169540524745/6736014906011025408\) \(63512118976120953338419200000000\) \([]\) \(123379200\) \(4.7996\) \(\Gamma_0(N)\)-optimal
43350.q1 43350s2 \([1, 1, 0, -420780770575, -105050158804422875]\) \(873851835888094527083289145/83719665273003835392\) \(789370780150013247671500800000000\) \([]\) \(370137600\) \(5.3489\)  

Rank

sage: E.rank()
 

The elliptic curves in class 43350s have rank \(0\).

Complex multiplication

The elliptic curves in class 43350s do not have complex multiplication.

Modular form 43350.2.a.s

sage: E.q_eigenform(10)
 
\(q - q^{2} - q^{3} + q^{4} + q^{6} + q^{7} - q^{8} + q^{9} - 3 q^{11} - q^{12} - 4 q^{13} - q^{14} + q^{16} - q^{18} - q^{19} + O(q^{20})\) 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.

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

Isogeny graph

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

The vertices are labelled with Cremona labels.