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Properties

Label 61347l
Number of curves $2$
Conductor $61347$
CM no
Rank $0$
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Show commands: SageMath
E = EllipticCurve("l1")
 
E.isogeny_class()
 

Elliptic curves in class 61347l

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
61347.g2 61347l1 \([1, 1, 1, 40472, -3939616]\) \(857375/1287\) \(-11005119726978663\) \([2]\) \(322560\) \(1.7635\) \(\Gamma_0(N)\)-optimal
61347.g1 61347l2 \([1, 1, 1, -266263, -39888958]\) \(244140625/61347\) \(524577373652649603\) \([2]\) \(645120\) \(2.1101\)  

Rank

sage: E.rank()
 

The elliptic curves in class 61347l have rank \(0\).

Complex multiplication

The elliptic curves in class 61347l do not have complex multiplication.

Modular form 61347.2.a.l

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