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Properties

Label 435120.i
Number of curves $6$
Conductor $435120$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("i1")
 
E.isogeny_class()
 

Elliptic curves in class 435120.i

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
435120.i1 435120i3 \([0, -1, 0, -267347936, 1682621243136]\) \(4385367890843575421521/24975000000\) \(12035210342400000000\) \([2]\) \(63700992\) \(3.2729\) \(\Gamma_0(N)\)-optimal*
435120.i2 435120i6 \([0, -1, 0, -237650016, -1403906400000]\) \(3080272010107543650001/15465841417699560\) \(7452839022391031949066240\) \([2]\) \(127401984\) \(3.6195\)  
435120.i3 435120i4 \([0, -1, 0, -22990816, 4773134080]\) \(2788936974993502801/1593609593601600\) \(767945011517991478886400\) \([2, 2]\) \(63700992\) \(3.2729\)  
435120.i4 435120i2 \([0, -1, 0, -16718816, 26263514880]\) \(1072487167529950801/2554882560000\) \(1231173133522698240000\) \([2, 2]\) \(31850496\) \(2.9263\) \(\Gamma_0(N)\)-optimal*
435120.i5 435120i1 \([0, -1, 0, -662496, 714698496]\) \(-66730743078481/419010969600\) \(-201917323519878758400\) \([2]\) \(15925248\) \(2.5798\) \(\Gamma_0(N)\)-optimal*
435120.i6 435120i5 \([0, -1, 0, 91316384, 37967944960]\) \(174751791402194852399/102423900876336360\) \(-49357084730163594926653440\) \([2]\) \(127401984\) \(3.6195\)  
*optimality has not been determined rigorously for conductors over 400000. In this case the optimal curve is certainly one of the 3 curves highlighted, and conditionally curve 435120.i1.

Rank

sage: E.rank()
 

The elliptic curves in class 435120.i have rank \(0\).

Complex multiplication

The elliptic curves in class 435120.i do not have complex multiplication.

Modular form 435120.2.a.i

sage: E.q_eigenform(10)
 
\(q - q^{3} - q^{5} + q^{9} - 4 q^{11} + 2 q^{13} + q^{15} - 2 q^{17} + 4 q^{19} + O(q^{20})\) 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 LMFDB numbering.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.