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SageMath
E = EllipticCurve("bk1")
E.isogeny_class()
Elliptic curves in class 298816bk
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
298816.bk2 | 298816bk1 | \([0, 0, 0, 3700, -7408]\) | \(21369234375/12456892\) | \(-3265499496448\) | \([2]\) | \(319488\) | \(1.0906\) | \(\Gamma_0(N)\)-optimal |
298816.bk1 | 298816bk2 | \([0, 0, 0, -14860, -59376]\) | \(1384331873625/795308122\) | \(208485252333568\) | \([2]\) | \(638976\) | \(1.4372\) |
Rank
sage: E.rank()
The elliptic curves in class 298816bk have rank \(0\).
Complex multiplication
The elliptic curves in class 298816bk do not have complex multiplication.Modular form 298816.2.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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.