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SageMath
E = EllipticCurve("t1")
E.isogeny_class()
Elliptic curves in class 59976t
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
59976.o1 | 59976t1 | \([0, 0, 0, -1911, 13034]\) | \(35152/17\) | \(373254158592\) | \([2]\) | \(69120\) | \(0.91406\) | \(\Gamma_0(N)\)-optimal |
59976.o2 | 59976t2 | \([0, 0, 0, 6909, 99470]\) | \(415292/289\) | \(-25381282784256\) | \([2]\) | \(138240\) | \(1.2606\) |
Rank
sage: E.rank()
The elliptic curves in class 59976t have rank \(0\).
Complex multiplication
The elliptic curves in class 59976t do not have complex multiplication.Modular form 59976.2.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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.