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SageMath
E = EllipticCurve("hj1")
E.isogeny_class()
Elliptic curves in class 273600.hj
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 273600.hj1 | 273600hj4 | \([0, 0, 0, -8942700, -10278254000]\) | \(26487576322129/44531250\) | \(132969600000000000000\) | \([2]\) | \(9437184\) | \(2.7567\) | |
| 273600.hj2 | 273600hj2 | \([0, 0, 0, -734700, -51086000]\) | \(14688124849/8122500\) | \(24253655040000000000\) | \([2, 2]\) | \(4718592\) | \(2.4101\) | |
| 273600.hj3 | 273600hj1 | \([0, 0, 0, -446700, 114226000]\) | \(3301293169/22800\) | \(68080435200000000\) | \([2]\) | \(2359296\) | \(2.0635\) | \(\Gamma_0(N)\)-optimal |
| 273600.hj4 | 273600hj3 | \([0, 0, 0, 2865300, -403886000]\) | \(871257511151/527800050\) | \(-1576002504499200000000\) | \([2]\) | \(9437184\) | \(2.7567\) |
Rank
sage: E.rank()
The elliptic curves in class 273600.hj have rank \(1\).
Complex multiplication
The elliptic curves in class 273600.hj do not have complex multiplication.Modular form 273600.2.a.hj
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.
