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SageMath
E = EllipticCurve("rl1")
E.isogeny_class()
Elliptic curves in class 176400.rl
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 176400.rl1 | 176400qg3 | \([0, 0, 0, -1179675, 493148250]\) | \(132304644/5\) | \(6861289680000000\) | \([2]\) | \(1769472\) | \(2.1248\) | |
| 176400.rl2 | 176400qg2 | \([0, 0, 0, -77175, 6945750]\) | \(148176/25\) | \(8576612100000000\) | \([2, 2]\) | \(884736\) | \(1.7782\) | |
| 176400.rl3 | 176400qg1 | \([0, 0, 0, -22050, -1157625]\) | \(55296/5\) | \(107207651250000\) | \([2]\) | \(442368\) | \(1.4316\) | \(\Gamma_0(N)\)-optimal |
| 176400.rl4 | 176400qg4 | \([0, 0, 0, 143325, 39359250]\) | \(237276/625\) | \(-857661210000000000\) | \([2]\) | \(1769472\) | \(2.1248\) |
Rank
sage: E.rank()
The elliptic curves in class 176400.rl have rank \(1\).
Complex multiplication
The elliptic curves in class 176400.rl do not have complex multiplication.Modular form 176400.2.a.rl
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.
