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Properties

Label 308550js
Number of curves $2$
Conductor $308550$
CM no
Rank $0$
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Show commands: SageMath
E = EllipticCurve("js1")
 
E.isogeny_class()
 

Elliptic curves in class 308550js

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
308550.js2 308550js1 \([1, 0, 0, 42287, -8873083]\) \(302111711/1404540\) \(-38878566983437500\) \([2]\) \(2764800\) \(1.8656\) \(\Gamma_0(N)\)-optimal
308550.js1 308550js2 \([1, 0, 0, -471963, -111208833]\) \(420021471169/50191650\) \(1389337026025781250\) \([2]\) \(5529600\) \(2.2122\)  

Rank

sage: E.rank()
 

The elliptic curves in class 308550js have rank \(0\).

Complex multiplication

The elliptic curves in class 308550js do not have complex multiplication.

Modular form 308550.2.a.js

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