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SageMath
E = EllipticCurve("j1")
E.isogeny_class()
Elliptic curves in class 60840.j
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
60840.j1 | 60840bf2 | \([0, 0, 0, -187083, 30964518]\) | \(3721734/25\) | \(4864311375206400\) | \([2]\) | \(414720\) | \(1.8448\) | |
60840.j2 | 60840bf1 | \([0, 0, 0, -4563, 1067742]\) | \(-108/5\) | \(-486431137520640\) | \([2]\) | \(207360\) | \(1.4982\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 60840.j have rank \(0\).
Complex multiplication
The elliptic curves in class 60840.j do not have complex multiplication.Modular form 60840.2.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.