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SageMath
E = EllipticCurve("t1")
E.isogeny_class()
Elliptic curves in class 27225.t
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
27225.t1 | 27225bx2 | \([1, -1, 1, -308210, 65629842]\) | \(15069223/81\) | \(17404306650732375\) | \([2]\) | \(270336\) | \(1.9603\) | |
27225.t2 | 27225bx1 | \([1, -1, 1, -8735, 2141142]\) | \(-343/9\) | \(-1933811850081375\) | \([2]\) | \(135168\) | \(1.6138\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 27225.t have rank \(1\).
Complex multiplication
The elliptic curves in class 27225.t do not have complex multiplication.Modular form 27225.2.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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.