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SageMath
E = EllipticCurve("j1")
E.isogeny_class()
Elliptic curves in class 1170j
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
1170.j2 | 1170j1 | \([1, -1, 1, -473, 4281]\) | \(-16022066761/998400\) | \(-727833600\) | \([2]\) | \(640\) | \(0.45457\) | \(\Gamma_0(N)\)-optimal |
1170.j1 | 1170j2 | \([1, -1, 1, -7673, 260601]\) | \(68523370149961/243360\) | \(177409440\) | \([2]\) | \(1280\) | \(0.80114\) |
Rank
sage: E.rank()
The elliptic curves in class 1170j have rank \(1\).
Complex multiplication
The elliptic curves in class 1170j do not have complex multiplication.Modular form 1170.2.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.