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SageMath
E = EllipticCurve("l1")
E.isogeny_class()
Elliptic curves in class 128018l
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
128018.f2 | 128018l1 | \([1, 0, 1, 190693, 12180342]\) | \(24167/16\) | \(-507724920222083344\) | \([]\) | \(2090880\) | \(2.0862\) | \(\Gamma_0(N)\)-optimal |
128018.f1 | 128018l2 | \([1, 0, 1, -3329802, 2401892348]\) | \(-128667913/4096\) | \(-129977579576853336064\) | \([]\) | \(6272640\) | \(2.6355\) |
Rank
sage: E.rank()
The elliptic curves in class 128018l have rank \(1\).
Complex multiplication
The elliptic curves in class 128018l do not have complex multiplication.Modular form 128018.2.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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.