Properties

Label 344850.fs
Number of curves $4$
Conductor $344850$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("fs1")
 
E.isogeny_class()
 

Elliptic curves in class 344850.fs

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
344850.fs1 344850fs4 \([1, 1, 1, -9196063, -10737570469]\) \(3107086841064961/570\) \(15777965156250\) \([2]\) \(11796480\) \(2.3682\)  
344850.fs2 344850fs3 \([1, 1, 1, -665563, -111471469]\) \(1177918188481/488703750\) \(13527632875839843750\) \([2]\) \(11796480\) \(2.3682\)  
344850.fs3 344850fs2 \([1, 1, 1, -574813, -167917969]\) \(758800078561/324900\) \(8993440139062500\) \([2, 2]\) \(5898240\) \(2.0216\)  
344850.fs4 344850fs1 \([1, 1, 1, -30313, -3478969]\) \(-111284641/123120\) \(-3408040473750000\) \([2]\) \(2949120\) \(1.6750\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 344850.fs have rank \(0\).

Complex multiplication

The elliptic curves in class 344850.fs do not have complex multiplication.

Modular form 344850.2.a.fs

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

\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.