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Properties

Label 3850w
Number of curves $2$
Conductor $3850$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("w1")
 
E.isogeny_class()
 

Elliptic curves in class 3850w

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
3850.v1 3850w1 \([1, -1, 1, -18930, -556303]\) \(384082046109/152649728\) \(298144000000000\) \([2]\) \(13440\) \(1.4757\) \(\Gamma_0(N)\)-optimal
3850.v2 3850w2 \([1, -1, 1, 61070, -4076303]\) \(12896863402851/11111230592\) \(-21701622250000000\) \([2]\) \(26880\) \(1.8222\)  

Rank

sage: E.rank()
 

The elliptic curves in class 3850w have rank \(0\).

Complex multiplication

The elliptic curves in class 3850w do not have complex multiplication.

Modular form 3850.2.a.w

sage: E.q_eigenform(10)
 
\(q + q^{2} + q^{4} + q^{7} + q^{8} - 3 q^{9} - q^{11} - 2 q^{13} + q^{14} + q^{16} + 4 q^{17} - 3 q^{18} + 4 q^{19} + O(q^{20})\) 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.

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

Isogeny graph

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

The vertices are labelled with Cremona labels.