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SageMath
E = EllipticCurve("r1")
E.isogeny_class()
Elliptic curves in class 48552.r
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
48552.r1 | 48552z4 | \([0, -1, 0, -52415185632, 4618866912554412]\) | \(322159999717985454060440834/4250799\) | \(210132898135308288\) | \([2]\) | \(39813120\) | \(4.3076\) | |
48552.r2 | 48552z3 | \([0, -1, 0, -3284376432, 71780641472268]\) | \(79260902459030376659234/842751810121431609\) | \(41660374971762593466405931008\) | \([2]\) | \(39813120\) | \(4.3076\) | |
48552.r3 | 48552z2 | \([0, -1, 0, -3275949192, 72170610317820]\) | \(157304700372188331121828/18069292138401\) | \(446616356630335167661056\) | \([2, 2]\) | \(19906560\) | \(3.9610\) | |
48552.r4 | 48552z1 | \([0, -1, 0, -204220212, 1133805926340]\) | \(-152435594466395827792/1646846627220711\) | \(-10176223768821040637839104\) | \([2]\) | \(9953280\) | \(3.6145\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 48552.r have rank \(1\).
Complex multiplication
The elliptic curves in class 48552.r do not have complex multiplication.Modular form 48552.2.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 LMFDB numbering.
\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.