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SageMath
E = EllipticCurve("q1")
E.isogeny_class()
Elliptic curves in class 23520.q
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
23520.q1 | 23520k4 | \([0, -1, 0, -15558545, -23615994303]\) | \(864335783029582144/59535\) | \(28689339248640\) | \([2]\) | \(737280\) | \(2.4832\) | |
23520.q2 | 23520k3 | \([0, -1, 0, -1092520, -271803608]\) | \(2394165105226952/854262178245\) | \(51457582596273154560\) | \([2]\) | \(737280\) | \(2.4832\) | |
23520.q3 | 23520k1 | \([0, -1, 0, -972470, -368707968]\) | \(13507798771700416/3544416225\) | \(26687809565121600\) | \([2, 2]\) | \(368640\) | \(2.1366\) | \(\Gamma_0(N)\)-optimal |
23520.q4 | 23520k2 | \([0, -1, 0, -853400, -462487500]\) | \(-1141100604753992/875529151875\) | \(-52738626144738240000\) | \([2]\) | \(737280\) | \(2.4832\) |
Rank
sage: E.rank()
The elliptic curves in class 23520.q have rank \(1\).
Complex multiplication
The elliptic curves in class 23520.q do not have complex multiplication.Modular form 23520.2.a.q
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.