Properties

Label 53040m
Number of curves $6$
Conductor $53040$
CM no
Rank $0$
Graph

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

Elliptic curves in class 53040m

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
53040.bb4 53040m1 \([0, -1, 0, -16575, -815850]\) \(31476797652269056/49725\) \(795600\) \([2]\) \(45056\) \(0.82665\) \(\Gamma_0(N)\)-optimal
53040.bb3 53040m2 \([0, -1, 0, -16580, -815328]\) \(1969080716416336/2472575625\) \(632979360000\) \([2, 2]\) \(90112\) \(1.1732\)  
53040.bb5 53040m3 \([0, -1, 0, -12160, -1264400]\) \(-194204905090564/566398828125\) \(-579992400000000\) \([2]\) \(180224\) \(1.5198\)  
53040.bb2 53040m4 \([0, -1, 0, -21080, -332928]\) \(1011710313226084/536724738225\) \(549606131942400\) \([2, 4]\) \(180224\) \(1.5198\)  
53040.bb6 53040m5 \([0, -1, 0, 80320, -2685408]\) \(27980756504588158/17683545112935\) \(-36215900391290880\) \([4]\) \(360448\) \(1.8664\)  
53040.bb1 53040m6 \([0, -1, 0, -194480, 32821152]\) \(397210600760070242/3536192675535\) \(7242122599495680\) \([4]\) \(360448\) \(1.8664\)  

Rank

sage: E.rank()
 

The elliptic curves in class 53040m have rank \(0\).

Complex multiplication

The elliptic curves in class 53040m do not have complex multiplication.

Modular form 53040.2.a.m

sage: E.q_eigenform(10)
 
\(q - q^{3} + q^{5} + q^{9} - 4q^{11} + q^{13} - q^{15} + q^{17} + 4q^{19} + O(q^{20})\)  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 Cremona numbering.

\(\left(\begin{array}{rrrrrr} 1 & 2 & 4 & 4 & 8 & 8 \\ 2 & 1 & 2 & 2 & 4 & 4 \\ 4 & 2 & 1 & 4 & 8 & 8 \\ 4 & 2 & 4 & 1 & 2 & 2 \\ 8 & 4 & 8 & 2 & 1 & 4 \\ 8 & 4 & 8 & 2 & 4 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.