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SageMath
E = EllipticCurve("r1")
E.isogeny_class()
Elliptic curves in class 24150r
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
24150.c1 | 24150r1 | \([1, 1, 0, -68575, 6197125]\) | \(18260010268037/1994194944\) | \(3894912000000000\) | \([2]\) | \(184320\) | \(1.7252\) | \(\Gamma_0(N)\)-optimal |
24150.c2 | 24150r2 | \([1, 1, 0, 91425, 30997125]\) | \(43269428370043/237036554496\) | \(-462962020500000000\) | \([2]\) | \(368640\) | \(2.0718\) |
Rank
sage: E.rank()
The elliptic curves in class 24150r have rank \(1\).
Complex multiplication
The elliptic curves in class 24150r do not have complex multiplication.Modular form 24150.2.a.r
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.