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Properties

Label 84150ev
Number of curves $2$
Conductor $84150$
CM no
Rank $1$
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Show commands: SageMath
E = EllipticCurve("ev1")
 
E.isogeny_class()
 

Elliptic curves in class 84150ev

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
84150.eo1 84150ev1 \([1, -1, 1, -44555, -3608553]\) \(858729462625/38148\) \(434529562500\) \([2]\) \(294912\) \(1.3104\) \(\Gamma_0(N)\)-optimal
84150.eo2 84150ev2 \([1, -1, 1, -42305, -3991053]\) \(-735091890625/181908738\) \(-2072054218781250\) \([2]\) \(589824\) \(1.6570\)  

Rank

sage: E.rank()
 

The elliptic curves in class 84150ev have rank \(1\).

Complex multiplication

The elliptic curves in class 84150ev do not have complex multiplication.

Modular form 84150.2.a.ev

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