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SageMath
E = EllipticCurve("bt1")
E.isogeny_class()
Elliptic curves in class 141610bt
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
141610.o2 | 141610bt1 | \([1, 1, 0, -35697, -2455991]\) | \(511981129/34300\) | \(337037361024700\) | \([]\) | \(497664\) | \(1.5366\) | \(\Gamma_0(N)\)-optimal |
141610.o1 | 141610bt2 | \([1, 1, 0, -531332, 148316176]\) | \(1688258640889/7000000\) | \(68783134903000000\) | \([]\) | \(1492992\) | \(2.0859\) |
Rank
sage: E.rank()
The elliptic curves in class 141610bt have rank \(2\).
Complex multiplication
The elliptic curves in class 141610bt do not have complex multiplication.Modular form 141610.2.a.bt
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 Cremona 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 Cremona labels.