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SageMath
E = EllipticCurve("a1")
E.isogeny_class()
Elliptic curves in class 95139.a
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
95139.a1 | 95139b2 | \([1, -1, 1, -16037, -773350]\) | \(19034163/121\) | \(2899474525827\) | \([2]\) | \(241920\) | \(1.2283\) | |
95139.a2 | 95139b1 | \([1, -1, 1, -1622, 5060]\) | \(19683/11\) | \(263588593257\) | \([2]\) | \(120960\) | \(0.88173\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 95139.a have rank \(1\).
Complex multiplication
The elliptic curves in class 95139.a do not have complex multiplication.Modular form 95139.2.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.