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SageMath
E = EllipticCurve("j1")
E.isogeny_class()
Elliptic curves in class 120240.j
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
120240.j1 | 120240bl2 | \([0, 0, 0, -81243, -8676342]\) | \(735580702683/22311200\) | \(1798763927961600\) | \([2]\) | \(460800\) | \(1.7034\) | |
120240.j2 | 120240bl1 | \([0, 0, 0, -12123, 323082]\) | \(2444008923/855040\) | \(68934665502720\) | \([2]\) | \(230400\) | \(1.3568\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 120240.j have rank \(0\).
Complex multiplication
The elliptic curves in class 120240.j do not have complex multiplication.Modular form 120240.2.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 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.