Properties

Label 35728.m
Number of curves $4$
Conductor $35728$
CM no
Rank $1$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("m1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 35728.m

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
35728.m1 35728y4 \([0, 0, 0, -853691, -303564886]\) \(16798320881842096017/2132227789307\) \(8733605025001472\) \([2]\) \(344064\) \(2.0807\)  
35728.m2 35728y3 \([0, 0, 0, -338651, 72754890]\) \(1048626554636928177/48569076788309\) \(198938938524913664\) \([4]\) \(344064\) \(2.0807\)  
35728.m3 35728y2 \([0, 0, 0, -57931, -3881670]\) \(5249244962308257/1448621666569\) \(5933554346266624\) \([2, 2]\) \(172032\) \(1.7341\)  
35728.m4 35728y1 \([0, 0, 0, 9349, -396566]\) \(22062729659823/29354283343\) \(-120235144572928\) \([2]\) \(86016\) \(1.3875\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 35728.m have rank \(1\).

Complex multiplication

The elliptic curves in class 35728.m do not have complex multiplication.

Modular form 35728.2.a.m

sage: E.q_eigenform(10)
 
\(q - 2q^{5} + q^{7} - 3q^{9} + q^{11} + 6q^{13} - 2q^{17} + 8q^{19} + O(q^{20})\)  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.