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SageMath
E = EllipticCurve("a1")
E.isogeny_class()
Elliptic curves in class 129960.a
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 129960.a1 | 129960bf4 | \([0, 0, 0, -347643, -78892218]\) | \(132304644/5\) | \(175597809914880\) | \([2]\) | \(884736\) | \(1.8193\) | |
| 129960.a2 | 129960bf2 | \([0, 0, 0, -22743, -1111158]\) | \(148176/25\) | \(219497262393600\) | \([2, 2]\) | \(442368\) | \(1.4727\) | |
| 129960.a3 | 129960bf1 | \([0, 0, 0, -6498, 185193]\) | \(55296/5\) | \(2743715779920\) | \([2]\) | \(221184\) | \(1.1262\) | \(\Gamma_0(N)\)-optimal |
| 129960.a4 | 129960bf3 | \([0, 0, 0, 42237, -6296562]\) | \(237276/625\) | \(-21949726239360000\) | \([2]\) | \(884736\) | \(1.8193\) |
Rank
sage: E.rank()
The elliptic curves in class 129960.a have rank \(1\).
Complex multiplication
The elliptic curves in class 129960.a do not have complex multiplication.Modular form 129960.2.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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
