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SageMath
E = EllipticCurve("a1")
E.isogeny_class()
Elliptic curves in class 43890a
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 43890.a3 | 43890a1 | \([1, 1, 0, -458, 3588]\) | \(10661073346729/351120\) | \(351120\) | \([2]\) | \(13312\) | \(0.15757\) | \(\Gamma_0(N)\)-optimal |
| 43890.a2 | 43890a2 | \([1, 1, 0, -478, 3232]\) | \(12117869279209/1926332100\) | \(1926332100\) | \([2, 2]\) | \(26624\) | \(0.50415\) | |
| 43890.a4 | 43890a3 | \([1, 1, 0, 852, 19458]\) | \(68272497696311/197159366250\) | \(-197159366250\) | \([2]\) | \(53248\) | \(0.85072\) | |
| 43890.a1 | 43890a4 | \([1, 1, 0, -2128, -35378]\) | \(1066491572492809/103257237930\) | \(103257237930\) | \([2]\) | \(53248\) | \(0.85072\) |
Rank
sage: E.rank()
The elliptic curves in class 43890a have rank \(2\).
Complex multiplication
The elliptic curves in class 43890a do not have complex multiplication.Modular form 43890.2.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.
