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SageMath
E = EllipticCurve("j1")
E.isogeny_class()
Elliptic curves in class 304920j
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
304920.j2 | 304920j1 | \([0, 0, 0, 2277, 111078]\) | \(1314036/6125\) | \(-6085715328000\) | \([2]\) | \(442368\) | \(1.1355\) | \(\Gamma_0(N)\)-optimal |
304920.j1 | 304920j2 | \([0, 0, 0, -25443, 1391742]\) | \(916628022/109375\) | \(217346976000000\) | \([2]\) | \(884736\) | \(1.4820\) |
Rank
sage: E.rank()
The elliptic curves in class 304920j have rank \(0\).
Complex multiplication
The elliptic curves in class 304920j do not have complex multiplication.Modular form 304920.2.a.j
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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.