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SageMath
E = EllipticCurve("t1")
E.isogeny_class()
Elliptic curves in class 24150t
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
24150.l2 | 24150t1 | \([1, 1, 0, -3950, 16500]\) | \(3491055413/1947456\) | \(3803625000000\) | \([2]\) | \(57600\) | \(1.1042\) | \(\Gamma_0(N)\)-optimal |
24150.l1 | 24150t2 | \([1, 1, 0, -38950, -2958500]\) | \(3346058125493/21595896\) | \(42179484375000\) | \([2]\) | \(115200\) | \(1.4508\) |
Rank
sage: E.rank()
The elliptic curves in class 24150t have rank \(1\).
Complex multiplication
The elliptic curves in class 24150t do not have complex multiplication.Modular form 24150.2.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.