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SageMath
E = EllipticCurve("t1")
E.isogeny_class()
Elliptic curves in class 3850t
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
3850.q2 | 3850t1 | \([1, 1, 1, -53, 3291]\) | \(-659361145/189314048\) | \(-4732851200\) | \([5]\) | \(2400\) | \(0.53569\) | \(\Gamma_0(N)\)-optimal |
3850.q1 | 3850t2 | \([1, 1, 1, -12513, -631469]\) | \(-22187592025/4509428\) | \(-44037382812500\) | \([]\) | \(12000\) | \(1.3404\) |
Rank
sage: E.rank()
The elliptic curves in class 3850t have rank \(0\).
Complex multiplication
The elliptic curves in class 3850t do not have complex multiplication.Modular form 3850.2.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.
\(\left(\begin{array}{rr} 1 & 5 \\ 5 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.