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SageMath
E = EllipticCurve("a1")
E.isogeny_class()
Elliptic curves in class 420.a
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
420.a1 | 420a1 | \([0, -1, 0, -4061, 67590]\) | \(463030539649024/149501953125\) | \(2392031250000\) | \([2]\) | \(840\) | \(1.0787\) | \(\Gamma_0(N)\)-optimal |
420.a2 | 420a2 | \([0, -1, 0, 11564, 448840]\) | \(667990736021936/732392128125\) | \(-187492384800000\) | \([2]\) | \(1680\) | \(1.4253\) |
Rank
sage: E.rank()
The elliptic curves in class 420.a have rank \(0\).
Complex multiplication
The elliptic curves in class 420.a do not have complex multiplication.Modular form 420.2.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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.