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SageMath
E = EllipticCurve("a1")
E.isogeny_class()
Elliptic curves in class 46546.a
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
46546.a1 | 46546a4 | \([1, 0, 1, -154726, -16200690]\) | \(159661140625/48275138\) | \(123860796464719442\) | \([2]\) | \(616896\) | \(1.9849\) | |
46546.a2 | 46546a3 | \([1, 0, 1, -141036, -20395306]\) | \(120920208625/19652\) | \(50421655389668\) | \([2]\) | \(308448\) | \(1.6384\) | |
46546.a3 | 46546a2 | \([1, 0, 1, -58896, 5495222]\) | \(8805624625/2312\) | \(5931959457608\) | \([2]\) | \(205632\) | \(1.4356\) | |
46546.a4 | 46546a1 | \([1, 0, 1, -4136, 63030]\) | \(3048625/1088\) | \(2791510332992\) | \([2]\) | \(102816\) | \(1.0891\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 46546.a have rank \(0\).
Complex multiplication
The elliptic curves in class 46546.a do not have complex multiplication.Modular form 46546.2.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.
\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.