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SageMath
E = EllipticCurve("e1")
E.isogeny_class()
Elliptic curves in class 48841e
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
48841.a1 | 48841e1 | \([1, 0, 0, -2907057, 1907335312]\) | \(23320116793/2873\) | \(334725861580473233\) | \([2]\) | \(1161216\) | \(2.3861\) | \(\Gamma_0(N)\)-optimal |
48841.a2 | 48841e2 | \([1, 0, 0, -2662852, 2241065865]\) | \(-17923019113/8254129\) | \(-961667400320699598409\) | \([2]\) | \(2322432\) | \(2.7326\) |
Rank
sage: E.rank()
The elliptic curves in class 48841e have rank \(1\).
Complex multiplication
The elliptic curves in class 48841e do not have complex multiplication.Modular form 48841.2.a.e
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.