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SageMath
E = EllipticCurve("j1")
E.isogeny_class()
Elliptic curves in class 304200j
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
304200.j1 | 304200j1 | \([0, 0, 0, -15015, -701350]\) | \(7304528/81\) | \(4151380896000\) | \([2]\) | \(589824\) | \(1.2355\) | \(\Gamma_0(N)\)-optimal |
304200.j2 | 304200j2 | \([0, 0, 0, -3315, -1766050]\) | \(-19652/6561\) | \(-1345047410304000\) | \([2]\) | \(1179648\) | \(1.5821\) |
Rank
sage: E.rank()
The elliptic curves in class 304200j have rank \(0\).
Complex multiplication
The elliptic curves in class 304200j do not have complex multiplication.Modular form 304200.2.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.