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SageMath
E = EllipticCurve("t1")
E.isogeny_class()
Elliptic curves in class 330330.t
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
330330.t1 | 330330t2 | \([1, 1, 0, -6825007, 5263484989]\) | \(14910731455066091/3547704615000\) | \(8365301905289293965000\) | \([2]\) | \(26763264\) | \(2.9179\) | |
330330.t2 | 330330t1 | \([1, 1, 0, 1001273, 516063541]\) | \(47081076443029/75959956800\) | \(-179109604745019748800\) | \([2]\) | \(13381632\) | \(2.5714\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 330330.t have rank \(0\).
Complex multiplication
The elliptic curves in class 330330.t do not have complex multiplication.Modular form 330330.2.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.