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SageMath
E = EllipticCurve("t1")
E.isogeny_class()
Elliptic curves in class 381150.t
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
381150.t1 | 381150t1 | \([1, -1, 0, -3812067, -8293001909]\) | \(-2509090441/10718750\) | \(-26171774959671386718750\) | \([]\) | \(41057280\) | \(2.9866\) | \(\Gamma_0(N)\)-optimal |
381150.t2 | 381150t2 | \([1, -1, 0, 33622308, 199954426216]\) | \(1721540467559/8070721400\) | \(-19706132174274425446875000\) | \([]\) | \(123171840\) | \(3.5359\) |
Rank
sage: E.rank()
The elliptic curves in class 381150.t have rank \(1\).
Complex multiplication
The elliptic curves in class 381150.t do not have complex multiplication.Modular form 381150.2.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 LMFDB 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 LMFDB labels.