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SageMath
E = EllipticCurve("j1")
E.isogeny_class()
Elliptic curves in class 40560.j
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
40560.j1 | 40560bh2 | \([0, -1, 0, -8694261, 12182645565]\) | \(-21752792449024/6591796875\) | \(-22024729467000000000000\) | \([]\) | \(3234816\) | \(3.0011\) | |
40560.j2 | 40560bh1 | \([0, -1, 0, 796779, -142418979]\) | \(16742875136/12301875\) | \(-41103431120494080000\) | \([]\) | \(1078272\) | \(2.4518\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 40560.j have rank \(0\).
Complex multiplication
The elliptic curves in class 40560.j do not have complex multiplication.Modular form 40560.2.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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.