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SageMath
E = EllipticCurve("j1")
E.isogeny_class()
Elliptic curves in class 1344.j
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
1344.j1 | 1344e1 | \([0, -1, 0, -376, 2338]\) | \(92100460096/20253807\) | \(1296243648\) | \([2]\) | \(960\) | \(0.46208\) | \(\Gamma_0(N)\)-optimal |
1344.j2 | 1344e2 | \([0, -1, 0, 839, 13273]\) | \(15926924096/28588707\) | \(-117099343872\) | \([2]\) | \(1920\) | \(0.80865\) |
Rank
sage: E.rank()
The elliptic curves in class 1344.j have rank \(0\).
Complex multiplication
The elliptic curves in class 1344.j do not have complex multiplication.Modular form 1344.2.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.