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SageMath
E = EllipticCurve("p1")
E.isogeny_class()
Elliptic curves in class 8280.p
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
8280.p1 | 8280l3 | \([0, 0, 0, -9507, -351106]\) | \(63649751618/1164375\) | \(1738402560000\) | \([2]\) | \(12288\) | \(1.1435\) | |
8280.p2 | 8280l2 | \([0, 0, 0, -1227, 8246]\) | \(273671716/119025\) | \(88851686400\) | \([2, 2]\) | \(6144\) | \(0.79696\) | |
8280.p3 | 8280l1 | \([0, 0, 0, -1047, 13034]\) | \(680136784/345\) | \(64385280\) | \([2]\) | \(3072\) | \(0.45039\) | \(\Gamma_0(N)\)-optimal |
8280.p4 | 8280l4 | \([0, 0, 0, 4173, 61166]\) | \(5382838942/4197615\) | \(-6267005614080\) | \([2]\) | \(12288\) | \(1.1435\) |
Rank
sage: E.rank()
The elliptic curves in class 8280.p have rank \(0\).
Complex multiplication
The elliptic curves in class 8280.p do not have complex multiplication.Modular form 8280.2.a.p
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 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
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.