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SageMath
E = EllipticCurve("j1")
E.isogeny_class()
Elliptic curves in class 24150j
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
24150.s4 | 24150j1 | \([1, 1, 0, -14975, -1156875]\) | \(-23771111713777/22848457968\) | \(-357007155750000\) | \([2]\) | \(122880\) | \(1.4886\) | \(\Gamma_0(N)\)-optimal |
24150.s3 | 24150j2 | \([1, 1, 0, -279475, -56966375]\) | \(154502321244119857/55101928644\) | \(860967635062500\) | \([2, 2]\) | \(245760\) | \(1.8351\) | |
24150.s2 | 24150j3 | \([1, 1, 0, -319725, -39538125]\) | \(231331938231569617/90942310746882\) | \(1420973605420031250\) | \([2]\) | \(491520\) | \(2.1817\) | |
24150.s1 | 24150j4 | \([1, 1, 0, -4471225, -3640912625]\) | \(632678989847546725777/80515134\) | \(1258048968750\) | \([2]\) | \(491520\) | \(2.1817\) |
Rank
sage: E.rank()
The elliptic curves in class 24150j have rank \(0\).
Complex multiplication
The elliptic curves in class 24150j do not have complex multiplication.Modular form 24150.2.a.j
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.