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SageMath
E = EllipticCurve("j1")
E.isogeny_class()
Elliptic curves in class 110670.j
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
110670.j1 | 110670k2 | \([1, 1, 0, -7217, -37779]\) | \(41580322225044121/23540365585800\) | \(23540365585800\) | \([2]\) | \(442368\) | \(1.2558\) | |
110670.j2 | 110670k1 | \([1, 1, 0, 1783, -3579]\) | \(626321182331879/370523160000\) | \(-370523160000\) | \([2]\) | \(221184\) | \(0.90920\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 110670.j have rank \(1\).
Complex multiplication
The elliptic curves in class 110670.j do not have complex multiplication.Modular form 110670.2.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.