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SageMath
E = EllipticCurve("f1")
E.isogeny_class()
Elliptic curves in class 53900f
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
53900.v2 | 53900f1 | \([0, 0, 0, 9800, -385875]\) | \(3538944/4235\) | \(-124560878750000\) | \([2]\) | \(110592\) | \(1.3909\) | \(\Gamma_0(N)\)-optimal |
53900.v1 | 53900f2 | \([0, 0, 0, -57575, -3687250]\) | \(44851536/13475\) | \(6341281100000000\) | \([2]\) | \(221184\) | \(1.7374\) |
Rank
sage: E.rank()
The elliptic curves in class 53900f have rank \(1\).
Complex multiplication
The elliptic curves in class 53900f do not have complex multiplication.Modular form 53900.2.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.