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SageMath
E = EllipticCurve("cg1")
E.isogeny_class()
Elliptic curves in class 226512.cg
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
226512.cg1 | 226512bc4 | \([0, 0, 0, -1135618275, 14728264733666]\) | \(30618029936661765625/3678951124992\) | \(19461109913369327129591808\) | \([2]\) | \(79626240\) | \(3.8772\) | |
226512.cg2 | 226512bc3 | \([0, 0, 0, -65087715, 269893096418]\) | \(-5764706497797625/2612665516032\) | \(-13820615998120689578016768\) | \([2]\) | \(39813120\) | \(3.5307\) | |
226512.cg3 | 226512bc2 | \([0, 0, 0, -31372275, -38534337358]\) | \(645532578015625/252306960048\) | \(1334666679327763261489152\) | \([2]\) | \(26542080\) | \(3.3279\) | |
226512.cg4 | 226512bc1 | \([0, 0, 0, 6263565, -4338413134]\) | \(5137417856375/4510142208\) | \(-23857988392005368020992\) | \([2]\) | \(13271040\) | \(2.9813\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 226512.cg have rank \(0\).
Complex multiplication
The elliptic curves in class 226512.cg do not have complex multiplication.Modular form 226512.2.a.cg
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.