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SageMath
E = EllipticCurve("ea1")
E.isogeny_class()
Elliptic curves in class 212160.ea
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 212160.ea1 | 212160fe3 | \([0, 1, 0, -28321, 1825055]\) | \(76668128804168/414375\) | \(13578240000\) | \([2]\) | \(425984\) | \(1.1385\) | |
| 212160.ea2 | 212160fe2 | \([0, 1, 0, -1801, 26999]\) | \(157814179264/10989225\) | \(45011865600\) | \([2, 2]\) | \(212992\) | \(0.79197\) | |
| 212160.ea3 | 212160fe1 | \([0, 1, 0, -356, -2190]\) | \(78183136576/16286595\) | \(1042342080\) | \([2]\) | \(106496\) | \(0.44539\) | \(\Gamma_0(N)\)-optimal |
| 212160.ea4 | 212160fe4 | \([0, 1, 0, 1599, 120159]\) | \(13789468792/196642485\) | \(-6443580948480\) | \([2]\) | \(425984\) | \(1.1385\) |
Rank
sage: E.rank()
The elliptic curves in class 212160.ea have rank \(1\).
Complex multiplication
The elliptic curves in class 212160.ea do not have complex multiplication.Modular form 212160.2.a.ea
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.
