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SageMath
E = EllipticCurve("ba1")
E.isogeny_class()
Elliptic curves in class 85176.ba
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
85176.ba1 | 85176a2 | \([0, 0, 0, -245895, 46932314]\) | \(49284342000/91\) | \(3036024246528\) | \([2]\) | \(258048\) | \(1.6514\) | |
85176.ba2 | 85176a1 | \([0, 0, 0, -15210, 749177]\) | \(-186624000/8281\) | \(-17267387902128\) | \([2]\) | \(129024\) | \(1.3048\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 85176.ba have rank \(1\).
Complex multiplication
The elliptic curves in class 85176.ba do not have complex multiplication.Modular form 85176.2.a.ba
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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.