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SageMath
E = EllipticCurve("qp1")
E.isogeny_class()
Elliptic curves in class 369600qp
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 369600.qp4 | 369600qp1 | \([0, 1, 0, -5052033, 296964063]\) | \(3481467828171481/2005331497785\) | \(8213837814927360000000\) | \([2]\) | \(23592960\) | \(2.8946\) | \(\Gamma_0(N)\)-optimal |
| 369600.qp2 | 369600qp2 | \([0, 1, 0, -57540033, 167576220063]\) | \(5143681768032498601/14238434358225\) | \(58320627131289600000000\) | \([2, 2]\) | \(47185920\) | \(3.2412\) | |
| 369600.qp1 | 369600qp3 | \([0, 1, 0, -920028033, 10740816612063]\) | \(21026497979043461623321/161783881875\) | \(662666780160000000000\) | \([2]\) | \(94371840\) | \(3.5877\) | |
| 369600.qp3 | 369600qp4 | \([0, 1, 0, -34860033, 301048020063]\) | \(-1143792273008057401/8897444448004035\) | \(-36443932459024527360000000\) | \([2]\) | \(94371840\) | \(3.5877\) |
Rank
sage: E.rank()
The elliptic curves in class 369600qp have rank \(1\).
Complex multiplication
The elliptic curves in class 369600qp do not have complex multiplication.Modular form 369600.2.a.qp
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.
