Properties

Label 390775bm
Number of curves $4$
Conductor $390775$
CM no
Rank $1$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("bm1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 390775bm

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
390775.bm4 390775bm1 \([1, -1, 0, 715783, -265847184]\) \(22062729659823/29354283343\) \(-53960970015946984375\) \([2]\) \(8257536\) \(2.4720\) \(\Gamma_0(N)\)-optimal
390775.bm3 390775bm2 \([1, -1, 0, -4435342, -2599306809]\) \(5249244962308257/1448621666569\) \(2662951413284004390625\) \([2, 2]\) \(16515072\) \(2.8186\)  
390775.bm2 390775bm3 \([1, -1, 0, -25927967, 48746574316]\) \(1048626554636928177/48569076788309\) \(89282864297933836578125\) \([2]\) \(33030144\) \(3.1652\)  
390775.bm1 390775bm4 \([1, -1, 0, -65360717, -203348417434]\) \(16798320881842096017/2132227789307\) \(3919601049752800671875\) \([2]\) \(33030144\) \(3.1652\)  

Rank

sage: E.rank()
 

The elliptic curves in class 390775bm have rank \(1\).

Complex multiplication

The elliptic curves in class 390775bm do not have complex multiplication.

Modular form 390775.2.a.bm

sage: E.q_eigenform(10)
 
\(q + q^{2} - q^{4} - 3q^{8} - 3q^{9} - q^{11} + 6q^{13} - q^{16} - 2q^{17} - 3q^{18} + 8q^{19} + O(q^{20})\)  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 Cremona numbering.

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

Isogeny graph

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

The vertices are labelled with Cremona labels.