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SageMath
E = EllipticCurve("bl1")
E.isogeny_class()
Elliptic curves in class 317898.bl
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
317898.bl1 | 317898bl2 | \([1, -1, 1, -893300, 325193793]\) | \(-545407363875/14\) | \(-2023588938042\) | \([]\) | \(2694384\) | \(1.8775\) | |
317898.bl2 | 317898bl1 | \([1, -1, 1, -10250, 513969]\) | \(-7414875/2744\) | \(-44069270206248\) | \([]\) | \(898128\) | \(1.3282\) | \(\Gamma_0(N)\)-optimal |
317898.bl3 | 317898bl3 | \([1, -1, 1, 78055, -5184647]\) | \(4492125/3584\) | \(-41961140219238912\) | \([]\) | \(2694384\) | \(1.8775\) |
Rank
sage: E.rank()
The elliptic curves in class 317898.bl have rank \(0\).
Complex multiplication
The elliptic curves in class 317898.bl do not have complex multiplication.Modular form 317898.2.a.bl
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.
\(\left(\begin{array}{rrr} 1 & 3 & 9 \\ 3 & 1 & 3 \\ 9 & 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.