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SageMath
E = EllipticCurve("f1")
E.isogeny_class()
Elliptic curves in class 40733f
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
40733.i2 | 40733f1 | \([1, 1, 0, 1841, -114552]\) | \(4657463/41503\) | \(-6143933501167\) | \([2]\) | \(73920\) | \(1.1352\) | \(\Gamma_0(N)\)-optimal |
40733.i1 | 40733f2 | \([1, 1, 0, -27254, -1610035]\) | \(15124197817/1294139\) | \(191579017354571\) | \([2]\) | \(147840\) | \(1.4817\) |
Rank
sage: E.rank()
The elliptic curves in class 40733f have rank \(1\).
Complex multiplication
The elliptic curves in class 40733f do not have complex multiplication.Modular form 40733.2.a.f
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.