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SageMath
E = EllipticCurve("w1")
E.isogeny_class()
Elliptic curves in class 33810.w
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 33810.w1 | 33810v4 | \([1, 1, 0, -90332, -9794574]\) | \(692895692874169/51420783750\) | \(6049603787403750\) | \([2]\) | \(294912\) | \(1.7740\) | |
| 33810.w2 | 33810v2 | \([1, 1, 0, -18302, 765024]\) | \(5763259856089/1143116100\) | \(134486466048900\) | \([2, 2]\) | \(147456\) | \(1.4274\) | |
| 33810.w3 | 33810v1 | \([1, 1, 0, -17322, 870276]\) | \(4886171981209/270480\) | \(31821701520\) | \([2]\) | \(73728\) | \(1.0808\) | \(\Gamma_0(N)\)-optimal |
| 33810.w4 | 33810v3 | \([1, 1, 0, 38048, 4608094]\) | \(51774168853511/107398242630\) | \(-12635295847176870\) | \([2]\) | \(294912\) | \(1.7740\) |
Rank
sage: E.rank()
The elliptic curves in class 33810.w have rank \(0\).
Complex multiplication
The elliptic curves in class 33810.w do not have complex multiplication.Modular form 33810.2.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.
