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SageMath
E = EllipticCurve("ir1")
E.isogeny_class()
Elliptic curves in class 485184ir
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 485184.ir3 | 485184ir1 | \([0, 1, 0, -3731777, 1622231583]\) | \(466025146777/177366672\) | \(2187426881674420420608\) | \([2]\) | \(22118400\) | \(2.7941\) | \(\Gamma_0(N)\)-optimal |
| 485184.ir2 | 485184ir2 | \([0, 1, 0, -26373697, -50984005345]\) | \(164503536215257/4178071044\) | \(51527295472912240214016\) | \([2, 2]\) | \(44236800\) | \(3.1407\) | |
| 485184.ir4 | 485184ir3 | \([0, 1, 0, 4354623, -162681448545]\) | \(740480746823/927484650666\) | \(-11438478460075168693223424\) | \([2]\) | \(88473600\) | \(3.4872\) | |
| 485184.ir1 | 485184ir4 | \([0, 1, 0, -419372737, -3305723454817]\) | \(661397832743623417/443352042\) | \(5467770036955120140288\) | \([2]\) | \(88473600\) | \(3.4872\) |
Rank
sage: E.rank()
The elliptic curves in class 485184ir have rank \(0\).
Complex multiplication
The elliptic curves in class 485184ir do not have complex multiplication.Modular form 485184.2.a.ir
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.
