Properties

Label 304200.fw
Number of curves $4$
Conductor $304200$
CM no
Rank $0$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("fw1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 304200.fw

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
304200.fw1 304200fw4 \([0, 0, 0, -316380675, -2166022849250]\) \(31103978031362/195\) \(21956961068640000000\) \([2]\) \(49545216\) \(3.3169\)  
304200.fw2 304200fw3 \([0, 0, 0, -27390675, -5427139250]\) \(20183398562/11567205\) \(1302464973630656160000000\) \([2]\) \(49545216\) \(3.3169\)  
304200.fw3 304200fw2 \([0, 0, 0, -19785675, -33801394250]\) \(15214885924/38025\) \(2140803704192400000000\) \([2, 2]\) \(24772608\) \(2.9703\)  
304200.fw4 304200fw1 \([0, 0, 0, -773175, -928781750]\) \(-3631696/24375\) \(-343077516697500000000\) \([2]\) \(12386304\) \(2.6237\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 304200.fw have rank \(0\).

Complex multiplication

The elliptic curves in class 304200.fw do not have complex multiplication.

Modular form 304200.2.a.fw

sage: E.q_eigenform(10)
 
\(q + 4q^{7} + 4q^{11} + 6q^{17} + O(q^{20})\)  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.