Show commands: SageMath
Rank
The elliptic curves in class 4080.bb have rank \(0\).
L-function data
Bad L-factors: |
| ||||||||||||||||||||||||
Good L-factors: |
| ||||||||||||||||||||||||
See L-function page for more information |
Complex multiplication
The elliptic curves in class 4080.bb do not have complex multiplication.Modular form 4080.2.a.bb
Isogeny 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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
The vertices are labelled with LMFDB labels.
Elliptic curves in class 4080.bb
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
4080.bb1 | 4080o3 | \([0, 1, 0, -4000, 27140]\) | \(6913728144004/3658971285\) | \(3746786595840\) | \([4]\) | \(6144\) | \(1.1042\) | |
4080.bb2 | 4080o2 | \([0, 1, 0, -2300, -42900]\) | \(5258429611216/47403225\) | \(12135225600\) | \([2, 2]\) | \(3072\) | \(0.75759\) | |
4080.bb3 | 4080o1 | \([0, 1, 0, -2295, -43092]\) | \(83587439220736/6885\) | \(110160\) | \([2]\) | \(1536\) | \(0.41102\) | \(\Gamma_0(N)\)-optimal |
4080.bb4 | 4080o4 | \([0, 1, 0, -680, -100572]\) | \(-34008619684/4228250625\) | \(-4329728640000\) | \([4]\) | \(6144\) | \(1.1042\) |