Show commands: SageMath
Rank
The elliptic curves in class 55860l have rank \(0\).
L-function data
Bad L-factors: |
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Good L-factors: |
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See L-function page for more information |
Complex multiplication
The elliptic curves in class 55860l do not have complex multiplication.Modular form 55860.2.a.l
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 Cremona numbering.
\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)
Isogeny graph
The vertices are labelled with Cremona labels.
Elliptic curves in class 55860l
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
55860.k4 | 55860l1 | \([0, -1, 0, -59845, -5614538]\) | \(12592337649664/1315845\) | \(2476925574480\) | \([2]\) | \(207360\) | \(1.4101\) | \(\Gamma_0(N)\)-optimal |
55860.k3 | 55860l2 | \([0, -1, 0, -64500, -4685400]\) | \(985329269584/252434475\) | \(7602857868614400\) | \([2]\) | \(414720\) | \(1.7567\) | |
55860.k2 | 55860l3 | \([0, -1, 0, -130405, 9938650]\) | \(130287139815424/52926616125\) | \(99628215367842000\) | \([2]\) | \(622080\) | \(1.9594\) | |
55860.k1 | 55860l4 | \([0, -1, 0, -1810860, 938221992]\) | \(21804712949838544/8680921875\) | \(261453255084000000\) | \([2]\) | \(1244160\) | \(2.3060\) |