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SageMath
E = EllipticCurve("a1")
E.isogeny_class()
Elliptic curves in class 57120.a
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 57120.a1 | 57120bj4 | \([0, -1, 0, -5696, 167220]\) | \(39924541407752/43848525\) | \(22450444800\) | \([4]\) | \(65536\) | \(0.90123\) | |
| 57120.a2 | 57120bj3 | \([0, -1, 0, -4016, -95784]\) | \(13994036429192/139453125\) | \(71400000000\) | \([2]\) | \(65536\) | \(0.90123\) | |
| 57120.a3 | 57120bj1 | \([0, -1, 0, -446, 1320]\) | \(153646158016/79655625\) | \(5097960000\) | \([2, 2]\) | \(32768\) | \(0.55466\) | \(\Gamma_0(N)\)-optimal |
| 57120.a4 | 57120bj2 | \([0, -1, 0, 1679, 8545]\) | \(127719486656/82654425\) | \(-338552524800\) | \([2]\) | \(65536\) | \(0.90123\) |
Rank
sage: E.rank()
The elliptic curves in class 57120.a have rank \(1\).
Complex multiplication
The elliptic curves in class 57120.a do not have complex multiplication.Modular form 57120.2.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 LMFDB numbering.
\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
