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Properties

Label 42350x
Number of curves $2$
Conductor $42350$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("x1")
 
E.isogeny_class()
 

Elliptic curves in class 42350x

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
42350.n2 42350x1 \([1, 1, 0, -35, -95]\) \(1638505/28\) \(84700\) \([]\) \(5184\) \(-0.25696\) \(\Gamma_0(N)\)-optimal
42350.n1 42350x2 \([1, 1, 0, -310, 1940]\) \(1094638105/21952\) \(66404800\) \([]\) \(15552\) \(0.29234\)  

Rank

sage: E.rank()
 

The elliptic curves in class 42350x have rank \(1\).

Complex multiplication

The elliptic curves in class 42350x do not have complex multiplication.

Modular form 42350.2.a.x

sage: E.q_eigenform(10)
 
\(q - q^{2} - q^{3} + q^{4} + q^{6} + q^{7} - q^{8} - 2 q^{9} - q^{12} - 4 q^{13} - q^{14} + q^{16} - 6 q^{17} + 2 q^{18} + 4 q^{19} + O(q^{20})\) 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.

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

Isogeny graph

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

The vertices are labelled with Cremona labels.