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SageMath
E = EllipticCurve("x1")
E.isogeny_class()
Elliptic curves in class 4928.x
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
4928.x1 | 4928t1 | \([0, 1, 0, -357, -2719]\) | \(-78843215872/539\) | \(-34496\) | \([]\) | \(960\) | \(0.051574\) | \(\Gamma_0(N)\)-optimal |
4928.x2 | 4928t2 | \([0, 1, 0, -197, -4999]\) | \(-13278380032/156590819\) | \(-10021812416\) | \([]\) | \(2880\) | \(0.60088\) | |
4928.x3 | 4928t3 | \([0, 1, 0, 1763, 128281]\) | \(9463555063808/115539436859\) | \(-7394523958976\) | \([]\) | \(8640\) | \(1.1502\) |
Rank
sage: E.rank()
The elliptic curves in class 4928.x have rank \(0\).
Complex multiplication
The elliptic curves in class 4928.x do not have complex multiplication.Modular form 4928.2.a.x
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.