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SageMath
E = EllipticCurve("p1")
E.isogeny_class()
Elliptic curves in class 6300.p
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 6300.p1 | 6300j4 | \([0, 0, 0, -411375, 101555750]\) | \(2640279346000/3087\) | \(9001692000000\) | \([2]\) | \(41472\) | \(1.7688\) | |
| 6300.p2 | 6300j3 | \([0, 0, 0, -25500, 1614125]\) | \(-10061824000/352947\) | \(-64324590750000\) | \([2]\) | \(20736\) | \(1.4223\) | |
| 6300.p3 | 6300j2 | \([0, 0, 0, -6375, 62750]\) | \(9826000/5103\) | \(14880348000000\) | \([2]\) | \(13824\) | \(1.2195\) | |
| 6300.p4 | 6300j1 | \([0, 0, 0, 1500, 7625]\) | \(2048000/1323\) | \(-241116750000\) | \([2]\) | \(6912\) | \(0.87295\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 6300.p have rank \(1\).
Complex multiplication
The elliptic curves in class 6300.p do not have complex multiplication.Modular form 6300.2.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.
\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
