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SageMath
E = EllipticCurve("bg1")
E.isogeny_class()
Elliptic curves in class 705600.bg
sage: E.isogeny_class().curves
LMFDB label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height |
---|---|---|---|---|---|---|
705600.bg1 | \([0, 0, 0, -247327500, 1584025450000]\) | \(-7620530425/526848\) | \(-115675415850516480000000000\) | \([]\) | \(238878720\) | \(3.7520\) |
705600.bg2 | \([0, 0, 0, 17272500, 2246650000]\) | \(2595575/1512\) | \(-331976639877120000000000\) | \([]\) | \(79626240\) | \(3.2027\) |
Rank
sage: E.rank()
The elliptic curves in class 705600.bg have rank \(0\).
Complex multiplication
The elliptic curves in class 705600.bg do not have complex multiplication.Modular form 705600.2.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.