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SageMath
E = EllipticCurve("p1")
E.isogeny_class()
Elliptic curves in class 15600p
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 15600.cx4 | 15600p1 | \([0, 1, 0, -57383, 4441488]\) | \(83587439220736/13990184325\) | \(3497546081250000\) | \([2]\) | \(73728\) | \(1.7037\) | \(\Gamma_0(N)\)-optimal |
| 15600.cx2 | 15600p2 | \([0, 1, 0, -877508, 316088988]\) | \(18681746265374416/693005625\) | \(2772022500000000\) | \([2, 2]\) | \(147456\) | \(2.0502\) | |
| 15600.cx1 | 15600p3 | \([0, 1, 0, -14040008, 20244113988]\) | \(19129597231400697604/26325\) | \(421200000000\) | \([2]\) | \(294912\) | \(2.3968\) | |
| 15600.cx3 | 15600p4 | \([0, 1, 0, -837008, 346625988]\) | \(-4053153720264484/903687890625\) | \(-14459006250000000000\) | \([2]\) | \(294912\) | \(2.3968\) |
Rank
sage: E.rank()
The elliptic curves in class 15600p have rank \(0\).
Complex multiplication
The elliptic curves in class 15600p do not have complex multiplication.Modular form 15600.2.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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
