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SageMath
E = EllipticCurve("b1")
E.isogeny_class()
Elliptic curves in class 350b
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
350.e2 | 350b1 | \([1, 0, 0, 112, 392]\) | \(397535/392\) | \(-153125000\) | \([3]\) | \(120\) | \(0.25755\) | \(\Gamma_0(N)\)-optimal |
350.e1 | 350b2 | \([1, 0, 0, -1138, -20858]\) | \(-417267265/235298\) | \(-91913281250\) | \([]\) | \(360\) | \(0.80685\) |
Rank
sage: E.rank()
The elliptic curves in class 350b have rank \(0\).
Complex multiplication
The elliptic curves in class 350b do not have complex multiplication.Modular form 350.2.a.b
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.