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SageMath
E = EllipticCurve("p1")
E.isogeny_class()
Elliptic curves in class 14144p
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
14144.f1 | 14144p1 | \([0, 1, 0, -3809, 89215]\) | \(23320116793/2873\) | \(753139712\) | \([2]\) | \(12288\) | \(0.72670\) | \(\Gamma_0(N)\)-optimal |
14144.f2 | 14144p2 | \([0, 1, 0, -3489, 105151]\) | \(-17923019113/8254129\) | \(-2163770392576\) | \([2]\) | \(24576\) | \(1.0733\) |
Rank
sage: E.rank()
The elliptic curves in class 14144p have rank \(1\).
Complex multiplication
The elliptic curves in class 14144p do not have complex multiplication.Modular form 14144.2.a.p
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.