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SageMath
E = EllipticCurve("w1")
E.isogeny_class()
Elliptic curves in class 46200.w
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 46200.w1 | 46200h4 | \([0, -1, 0, -1948408, 407306812]\) | \(51126217658776516/25121936269815\) | \(401950980317040000000\) | \([4]\) | \(1474560\) | \(2.6468\) | |
| 46200.w2 | 46200h2 | \([0, -1, 0, -1040908, -403998188]\) | \(31181799673942864/387562277025\) | \(1550249108100000000\) | \([2, 2]\) | \(737280\) | \(2.3002\) | |
| 46200.w3 | 46200h1 | \([0, -1, 0, -1037783, -406573188]\) | \(494428821070157824/77818125\) | \(19454531250000\) | \([2]\) | \(368640\) | \(1.9536\) | \(\Gamma_0(N)\)-optimal |
| 46200.w4 | 46200h3 | \([0, -1, 0, -183408, -1050553188]\) | \(-42644293386916/29777663954115\) | \(-476442623265840000000\) | \([2]\) | \(1474560\) | \(2.6468\) |
Rank
sage: E.rank()
The elliptic curves in class 46200.w have rank \(0\).
Complex multiplication
The elliptic curves in class 46200.w do not have complex multiplication.Modular form 46200.2.a.w
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.
