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SageMath
E = EllipticCurve("j1")
E.isogeny_class()
Elliptic curves in class 10080j
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
10080.h3 | 10080j1 | \([0, 0, 0, -7353, -242352]\) | \(942344950464/1500625\) | \(70013160000\) | \([2, 2]\) | \(12288\) | \(0.97876\) | \(\Gamma_0(N)\)-optimal |
10080.h1 | 10080j2 | \([0, 0, 0, -117603, -15523002]\) | \(481927184300808/1225\) | \(457228800\) | \([2]\) | \(24576\) | \(1.3253\) | |
10080.h2 | 10080j3 | \([0, 0, 0, -9603, -81702]\) | \(262389836808/144120025\) | \(53792511091200\) | \([2]\) | \(24576\) | \(1.3253\) | |
10080.h4 | 10080j4 | \([0, 0, 0, -5148, -390528]\) | \(-5053029696/19140625\) | \(-57153600000000\) | \([2]\) | \(24576\) | \(1.3253\) |
Rank
sage: E.rank()
The elliptic curves in class 10080j have rank \(0\).
Complex multiplication
The elliptic curves in class 10080j do not have complex multiplication.Modular form 10080.2.a.j
sage: E.q_eigenform(10)
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 2 & 2 \\ 2 & 1 & 4 & 4 \\ 2 & 4 & 1 & 4 \\ 2 & 4 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.