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SageMath
E = EllipticCurve("bg1")
E.isogeny_class()
Elliptic curves in class 161472.bg
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
161472.bg1 | 161472bu2 | \([0, -1, 0, -350449185, 2532644547009]\) | \(-30526075007211889/103499257854\) | \(-16138573519978918873399296\) | \([]\) | \(31610880\) | \(3.7010\) | |
161472.bg2 | 161472bu1 | \([0, -1, 0, -54945, -1711778751]\) | \(-117649/8118144\) | \(-1265857036140209504256\) | \([]\) | \(4515840\) | \(2.7281\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 161472.bg have rank \(0\).
Complex multiplication
The elliptic curves in class 161472.bg do not have complex multiplication.Modular form 161472.2.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.
\(\left(\begin{array}{rr} 1 & 7 \\ 7 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.