Show commands: SageMath
Rank
The elliptic curves in class 91728.dp 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 91728.dp do not have complex multiplication.Modular form 91728.2.a.dp
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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
The vertices are labelled with LMFDB labels.
Elliptic curves in class 91728.dp
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
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91728.dp1 | 91728be1 | \([0, 0, 0, -89670, -10263589]\) | \(58107136000/464373\) | \(637239534514128\) | \([2]\) | \(294912\) | \(1.6682\) | \(\Gamma_0(N)\)-optimal |
91728.dp2 | 91728be2 | \([0, 0, 0, -30135, -23682778]\) | \(-137842000/10955763\) | \(-240546123546962688\) | \([2]\) | \(589824\) | \(2.0148\) |