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SageMath
E = EllipticCurve("ea1")
E.isogeny_class()
Elliptic curves in class 212160ea
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
212160.bo1 | 212160ea1 | \([0, -1, 0, -12356781, 16722816525]\) | \(203769809659907949070336/2016474841511325\) | \(2064870237707596800\) | \([2]\) | \(8110080\) | \(2.6743\) | \(\Gamma_0(N)\)-optimal |
212160.bo2 | 212160ea2 | \([0, -1, 0, -12062001, 17558282001]\) | \(-11845731628994222232016/1269935194601506875\) | \(-20806618228351088640000\) | \([2]\) | \(16220160\) | \(3.0208\) |
Rank
sage: E.rank()
The elliptic curves in class 212160ea have rank \(0\).
Complex multiplication
The elliptic curves in class 212160ea 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 Cremona numbering.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.