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SageMath
E = EllipticCurve("r1")
E.isogeny_class()
Elliptic curves in class 85176.r
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
85176.r1 | 85176i2 | \([0, 0, 0, -168831, -26693550]\) | \(21882096/7\) | \(170250898132224\) | \([2]\) | \(442368\) | \(1.7055\) | |
85176.r2 | 85176i1 | \([0, 0, 0, -9126, -533871]\) | \(-55296/49\) | \(-74484767932848\) | \([2]\) | \(221184\) | \(1.3589\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 85176.r have rank \(0\).
Complex multiplication
The elliptic curves in class 85176.r do not have complex multiplication.Modular form 85176.2.a.r
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.