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SageMath
E = EllipticCurve("bg1")
E.isogeny_class()
Elliptic curves in class 33810.bg
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
33810.bg1 | 33810bb2 | \([1, 0, 1, -449699, -27122434]\) | \(85486955243540761/46777901234400\) | \(5503373302325925600\) | \([2]\) | \(614400\) | \(2.2867\) | |
33810.bg2 | 33810bb1 | \([1, 0, 1, -269379, 53444542]\) | \(18374873741826841/136564270080\) | \(16066649810641920\) | \([2]\) | \(307200\) | \(1.9402\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 33810.bg have rank \(1\).
Complex multiplication
The elliptic curves in class 33810.bg do not have complex multiplication.Modular form 33810.2.a.bg
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.