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SageMath
E = EllipticCurve("bg1")
E.isogeny_class()
Elliptic curves in class 260100.bg
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
260100.bg1 | 260100bg1 | \([0, 0, 0, -411825, -183623375]\) | \(-1755904/2295\) | \(-10095870125823750000\) | \([]\) | \(3981312\) | \(2.3395\) | \(\Gamma_0(N)\)-optimal |
260100.bg2 | 260100bg2 | \([0, 0, 0, 3489675, 3530604625]\) | \(1068359936/1842375\) | \(-8104740184341843750000\) | \([]\) | \(11943936\) | \(2.8888\) |
Rank
sage: E.rank()
The elliptic curves in class 260100.bg have rank \(1\).
Complex multiplication
The elliptic curves in class 260100.bg do not have complex multiplication.Modular form 260100.2.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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.