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Properties

Label 23595n
Number of curves $8$
Conductor $23595$
CM no
Rank $0$
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Show commands: SageMath
E = EllipticCurve("n1")
 
E.isogeny_class()
 

Elliptic curves in class 23595n

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
23595.p6 23595n1 \([1, 0, 1, -13313, -592297]\) \(147281603041/5265\) \(9327268665\) \([2]\) \(30720\) \(1.0021\) \(\Gamma_0(N)\)-optimal
23595.p5 23595n2 \([1, 0, 1, -13918, -535669]\) \(168288035761/27720225\) \(49108069521225\) \([2, 2]\) \(61440\) \(1.3486\)  
23595.p7 23595n3 \([1, 0, 1, 25407, -3005279]\) \(1023887723039/2798036865\) \(-4956892986596265\) \([2]\) \(122880\) \(1.6952\)  
23595.p4 23595n4 \([1, 0, 1, -62923, 5560553]\) \(15551989015681/1445900625\) \(2561501157125625\) \([2, 2]\) \(122880\) \(1.6952\)  
23595.p8 23595n5 \([1, 0, 1, 73202, 26360453]\) \(24487529386319/183539412225\) \(-325151264660733225\) \([2]\) \(245760\) \(2.0418\)  
23595.p2 23595n6 \([1, 0, 1, -983128, 375114881]\) \(59319456301170001/594140625\) \(1052556359765625\) \([2, 2]\) \(245760\) \(2.0418\)  
23595.p3 23595n7 \([1, 0, 1, -959533, 393981443]\) \(-55150149867714721/5950927734375\) \(-10542431488037109375\) \([2]\) \(491520\) \(2.3884\)  
23595.p1 23595n8 \([1, 0, 1, -15730003, 24011406131]\) \(242970740812818720001/24375\) \(43181799375\) \([2]\) \(491520\) \(2.3884\)  

Rank

sage: E.rank()
 

The elliptic curves in class 23595n have rank \(0\).

Complex multiplication

The elliptic curves in class 23595n do not have complex multiplication.

Modular form 23595.2.a.n

sage: E.q_eigenform(10)
 
\(q + q^{2} + q^{3} - q^{4} + q^{5} + q^{6} - 3 q^{8} + q^{9} + q^{10} - q^{12} - q^{13} + q^{15} - q^{16} - 2 q^{17} + q^{18} + 4 q^{19} + O(q^{20})\) 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 Cremona numbering.

\(\left(\begin{array}{rrrrrrrr} 1 & 2 & 4 & 4 & 8 & 8 & 16 & 16 \\ 2 & 1 & 2 & 2 & 4 & 4 & 8 & 8 \\ 4 & 2 & 1 & 4 & 8 & 8 & 16 & 16 \\ 4 & 2 & 4 & 1 & 2 & 2 & 4 & 4 \\ 8 & 4 & 8 & 2 & 1 & 4 & 8 & 8 \\ 8 & 4 & 8 & 2 & 4 & 1 & 2 & 2 \\ 16 & 8 & 16 & 4 & 8 & 2 & 1 & 4 \\ 16 & 8 & 16 & 4 & 8 & 2 & 4 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.