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SageMath
E = EllipticCurve("bk1")
E.isogeny_class()
Elliptic curves in class 277725bk
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
277725.bk1 | 277725bk1 | \([0, -1, 1, -80883, -8828332]\) | \(-7079867613184/1250235\) | \(-10333973671875\) | \([]\) | \(746496\) | \(1.5020\) | \(\Gamma_0(N)\)-optimal |
277725.bk2 | 277725bk2 | \([0, -1, 1, 22617, -29450707]\) | \(154786758656/45397807875\) | \(-375241255716796875\) | \([]\) | \(2239488\) | \(2.0514\) |
Rank
sage: E.rank()
The elliptic curves in class 277725bk have rank \(1\).
Complex multiplication
The elliptic curves in class 277725bk do not have complex multiplication.Modular form 277725.2.a.bk
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.