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SageMath
E = EllipticCurve("cc1")
E.isogeny_class()
Elliptic curves in class 24990.cc
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 24990.cc1 | 24990cd4 | \([1, 0, 0, -320510, 69813372]\) | \(30949975477232209/478125000\) | \(56250928125000\) | \([2]\) | \(221184\) | \(1.7735\) | |
| 24990.cc2 | 24990cd2 | \([1, 0, 0, -20630, 1020900]\) | \(8253429989329/936360000\) | \(110161817640000\) | \([2, 2]\) | \(110592\) | \(1.4269\) | |
| 24990.cc3 | 24990cd1 | \([1, 0, 0, -4950, -117468]\) | \(114013572049/15667200\) | \(1843230412800\) | \([2]\) | \(55296\) | \(1.0803\) | \(\Gamma_0(N)\)-optimal |
| 24990.cc4 | 24990cd3 | \([1, 0, 0, 28370, 5146700]\) | \(21464092074671/109596256200\) | \(-12893889945673800\) | \([2]\) | \(221184\) | \(1.7735\) |
Rank
sage: E.rank()
The elliptic curves in class 24990.cc have rank \(1\).
Complex multiplication
The elliptic curves in class 24990.cc do not have complex multiplication.Modular form 24990.2.a.cc
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.
