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SageMath
E = EllipticCurve("l1")
E.isogeny_class()
Elliptic curves in class 22743l
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
22743.i2 | 22743l1 | \([1, -1, 1, -178763, 11264514]\) | \(2685619/1323\) | \(311221635813818793\) | \([2]\) | \(364800\) | \(2.0498\) | \(\Gamma_0(N)\)-optimal |
22743.i1 | 22743l2 | \([1, -1, 1, -2339348, 1376754234]\) | \(6018636259/5103\) | \(1200426309567586773\) | \([2]\) | \(729600\) | \(2.3963\) |
Rank
sage: E.rank()
The elliptic curves in class 22743l have rank \(0\).
Complex multiplication
The elliptic curves in class 22743l do not have complex multiplication.Modular form 22743.2.a.l
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.