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SageMath
E = EllipticCurve("t1")
E.isogeny_class()
Elliptic curves in class 5200t
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
5200.i2 | 5200t1 | \([0, 1, 0, -2088, 45748]\) | \(-9836106385/3407872\) | \(-348966092800\) | \([]\) | \(8640\) | \(0.92623\) | \(\Gamma_0(N)\)-optimal |
5200.i1 | 5200t2 | \([0, 1, 0, -181288, 29649588]\) | \(-6434774386429585/140608\) | \(-14398259200\) | \([]\) | \(25920\) | \(1.4755\) |
Rank
sage: E.rank()
The elliptic curves in class 5200t have rank \(0\).
Complex multiplication
The elliptic curves in class 5200t do not have complex multiplication.Modular form 5200.2.a.t
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.