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Properties

Label 1342c
Number of curves $3$
Conductor $1342$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("c1")
 
E.isogeny_class()
 

Elliptic curves in class 1342c

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
1342.b3 1342c1 \([1, 1, 1, -13960, 629001]\) \(300872095888141441/22515023872\) \(22515023872\) \([5]\) \(3200\) \(1.0360\) \(\Gamma_0(N)\)-optimal
1342.b2 1342c2 \([1, 1, 1, -187880, -31262199]\) \(733441552889589371521/4352738523915232\) \(4352738523915232\) \([5]\) \(16000\) \(1.8407\)  
1342.b1 1342c3 \([1, 1, 1, -117257250, -488766109679]\) \(178296503348692983836197044001/1342\) \(1342\) \([]\) \(80000\) \(2.6454\)  

Rank

sage: E.rank()
 

The elliptic curves in class 1342c have rank \(0\).

Complex multiplication

The elliptic curves in class 1342c do not have complex multiplication.

Modular form 1342.2.a.c

sage: E.q_eigenform(10)
 
\(q + q^{2} - q^{3} + q^{4} - 4 q^{5} - q^{6} - 2 q^{7} + q^{8} - 2 q^{9} - 4 q^{10} + q^{11} - q^{12} - q^{13} - 2 q^{14} + 4 q^{15} + q^{16} + 3 q^{17} - 2 q^{18} + O(q^{20})\) 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.

\(\left(\begin{array}{rrr} 1 & 5 & 25 \\ 5 & 1 & 5 \\ 25 & 5 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.