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SageMath
E = EllipticCurve("a1")
E.isogeny_class()
Elliptic curves in class 28577a
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 28577.a4 | 28577a1 | \([1, -1, 1, -1156, 6750]\) | \(35937/17\) | \(80751772097\) | \([2]\) | \(17280\) | \(0.78700\) | \(\Gamma_0(N)\)-optimal |
| 28577.a2 | 28577a2 | \([1, -1, 1, -9561, -352984]\) | \(20346417/289\) | \(1372780125649\) | \([2, 2]\) | \(34560\) | \(1.1336\) | |
| 28577.a3 | 28577a3 | \([1, -1, 1, -1156, -958144]\) | \(-35937/83521\) | \(-396733456312561\) | \([2]\) | \(69120\) | \(1.4802\) | |
| 28577.a1 | 28577a4 | \([1, -1, 1, -152446, -22871660]\) | \(82483294977/17\) | \(80751772097\) | \([2]\) | \(69120\) | \(1.4802\) |
Rank
sage: E.rank()
The elliptic curves in class 28577a have rank \(1\).
Complex multiplication
The elliptic curves in class 28577a do not have complex multiplication.Modular form 28577.2.a.a
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.
