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SageMath
E = EllipticCurve("p1")
E.isogeny_class()
Elliptic curves in class 116160p
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
116160.ba5 | 116160p1 | \([0, -1, 0, 38559, -11314719]\) | \(13651919/126720\) | \(-58849285877268480\) | \([2]\) | \(737280\) | \(1.8990\) | \(\Gamma_0(N)\)-optimal |
116160.ba4 | 116160p2 | \([0, -1, 0, -580961, -157397535]\) | \(46694890801/3920400\) | \(1820649781827993600\) | \([2, 2]\) | \(1474560\) | \(2.2456\) | |
116160.ba3 | 116160p3 | \([0, -1, 0, -1974881, 887763681]\) | \(1834216913521/329422500\) | \(152985155278602240000\) | \([2, 2]\) | \(2949120\) | \(2.5922\) | |
116160.ba2 | 116160p4 | \([0, -1, 0, -9099361, -10561771295]\) | \(179415687049201/1443420\) | \(670330146945761280\) | \([2]\) | \(2949120\) | \(2.5922\) | |
116160.ba6 | 116160p5 | \([0, -1, 0, 3833119, 5119472481]\) | \(13411719834479/32153832150\) | \(-14932371056226769305600\) | \([2]\) | \(5898240\) | \(2.9388\) | |
116160.ba1 | 116160p6 | \([0, -1, 0, -30085601, 63524069985]\) | \(6484907238722641/283593750\) | \(131702096486400000000\) | \([2]\) | \(5898240\) | \(2.9388\) |
Rank
sage: E.rank()
The elliptic curves in class 116160p have rank \(0\).
Complex multiplication
The elliptic curves in class 116160p do not have complex multiplication.Modular form 116160.2.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 Cremona numbering.
\(\left(\begin{array}{rrrrrr} 1 & 2 & 4 & 4 & 8 & 8 \\ 2 & 1 & 2 & 2 & 4 & 4 \\ 4 & 2 & 1 & 4 & 2 & 2 \\ 4 & 2 & 4 & 1 & 8 & 8 \\ 8 & 4 & 2 & 8 & 1 & 4 \\ 8 & 4 & 2 & 8 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.