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SageMath
E = EllipticCurve("l1")
E.isogeny_class()
Elliptic curves in class 116242l
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
116242.c2 | 116242l1 | \([1, 0, 1, -501823942, 4326806219160]\) | \(297068250173962064073697/2799978137191424\) | \(131727438244909407724544\) | \([2]\) | \(35481600\) | \(3.5990\) | \(\Gamma_0(N)\)-optimal |
116242.c1 | 116242l2 | \([1, 0, 1, -8029164902, 276918920808216]\) | \(1216783295219854805382860257/108097620512\) | \(5085547790990711072\) | \([2]\) | \(70963200\) | \(3.9455\) |
Rank
sage: E.rank()
The elliptic curves in class 116242l have rank \(0\).
Complex multiplication
The elliptic curves in class 116242l do not have complex multiplication.Modular form 116242.2.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.