Properties

Label 247962.f
Number of curves $4$
Conductor $247962$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("f1")
 
E.isogeny_class()
 

Elliptic curves in class 247962.f

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
247962.f1 247962f3 \([1, 1, 0, -952318730, -11310025748268]\) \(3957101249824708884951625/772310238681366528\) \(18641691675577953583890432\) \([2]\) \(131383296\) \(3.8487\)  
247962.f2 247962f4 \([1, 1, 0, -851700490, -13793102798636]\) \(-2830680648734534916567625/1766676274677722124288\) \(-42643270480696470537828175872\) \([2]\) \(262766592\) \(4.1952\)  
247962.f3 247962f1 \([1, 1, 0, -28994075, 38899354269]\) \(111675519439697265625/37528570137307392\) \(905848451160596648610048\) \([2]\) \(43794432\) \(3.2994\) \(\Gamma_0(N)\)-optimal
247962.f4 247962f2 \([1, 1, 0, 84594485, 268961623693]\) \(2773679829880629422375/2899504554614368272\) \(-69986991252818582556810768\) \([2]\) \(87588864\) \(3.6459\)  

Rank

sage: E.rank()
 

The elliptic curves in class 247962.f have rank \(0\).

Complex multiplication

The elliptic curves in class 247962.f do not have complex multiplication.

Modular form 247962.2.a.f

sage: E.q_eigenform(10)
 
\(q - q^{2} - q^{3} + q^{4} + q^{6} + 4 q^{7} - q^{8} + q^{9} - q^{11} - q^{12} + q^{13} - 4 q^{14} + q^{16} - q^{18} + 2 q^{19} + O(q^{20})\) 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 LMFDB numbering.

\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.