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SageMath
E = EllipticCurve("bx1")
E.isogeny_class()
Elliptic curves in class 23520.bx
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
23520.bx1 | 23520w4 | \([0, 1, 0, -15558545, 23615994303]\) | \(864335783029582144/59535\) | \(28689339248640\) | \([2]\) | \(737280\) | \(2.4832\) | |
23520.bx2 | 23520w3 | \([0, 1, 0, -1092520, 271803608]\) | \(2394165105226952/854262178245\) | \(51457582596273154560\) | \([2]\) | \(737280\) | \(2.4832\) | |
23520.bx3 | 23520w1 | \([0, 1, 0, -972470, 368707968]\) | \(13507798771700416/3544416225\) | \(26687809565121600\) | \([2, 2]\) | \(368640\) | \(2.1366\) | \(\Gamma_0(N)\)-optimal |
23520.bx4 | 23520w2 | \([0, 1, 0, -853400, 462487500]\) | \(-1141100604753992/875529151875\) | \(-52738626144738240000\) | \([2]\) | \(737280\) | \(2.4832\) |
Rank
sage: E.rank()
The elliptic curves in class 23520.bx have rank \(0\).
Complex multiplication
The elliptic curves in class 23520.bx do not have complex multiplication.Modular form 23520.2.a.bx
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.