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Elliptic curves in class 72.a
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
72.a1 | 72a5 | \([0, 0, 0, -3459, 78302]\) | \(3065617154/9\) | \(13436928\) | \([2]\) | \(32\) | \(0.59710\) | |
72.a2 | 72a3 | \([0, 0, 0, -579, -5362]\) | \(28756228/3\) | \(2239488\) | \([2]\) | \(16\) | \(0.25053\) | |
72.a3 | 72a4 | \([0, 0, 0, -219, 1190]\) | \(1556068/81\) | \(60466176\) | \([2, 2]\) | \(16\) | \(0.25053\) | |
72.a4 | 72a2 | \([0, 0, 0, -39, -70]\) | \(35152/9\) | \(1679616\) | \([2, 2]\) | \(8\) | \(-0.096046\) | |
72.a5 | 72a1 | \([0, 0, 0, 6, -7]\) | \(2048/3\) | \(-34992\) | \([4]\) | \(4\) | \(-0.44262\) | \(\Gamma_0(N)\)-optimal |
72.a6 | 72a6 | \([0, 0, 0, 141, 4718]\) | \(207646/6561\) | \(-9795520512\) | \([2]\) | \(32\) | \(0.59710\) |
Rank
The elliptic curves in class 72.a have rank \(0\).
Complex multiplication
The elliptic curves in class 72.a do not have complex multiplication.Modular form 72.2.a.a
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.
\(\left(\begin{array}{rrrrrr} 1 & 8 & 2 & 4 & 8 & 4 \\ 8 & 1 & 4 & 2 & 4 & 8 \\ 2 & 4 & 1 & 2 & 4 & 2 \\ 4 & 2 & 2 & 1 & 2 & 4 \\ 8 & 4 & 4 & 2 & 1 & 8 \\ 4 & 8 & 2 & 4 & 8 & 1 \end{array}\right)\)
Isogeny graph
The vertices are labelled with LMFDB labels.