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SageMath
E = EllipticCurve("cg1")
E.isogeny_class()
Elliptic curves in class 223440cg
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 223440.em3 | 223440cg1 | \([0, 1, 0, -10331176, -12782880076]\) | \(253060782505556761/41184460800\) | \(19846392334988083200\) | \([2]\) | \(7077888\) | \(2.7119\) | \(\Gamma_0(N)\)-optimal |
| 223440.em2 | 223440cg2 | \([0, 1, 0, -11334696, -10150847820]\) | \(334199035754662681/101099003040000\) | \(48718629309042524160000\) | \([2, 2]\) | \(14155776\) | \(3.0585\) | |
| 223440.em1 | 223440cg3 | \([0, 1, 0, -69727016, 216247855284]\) | \(77799851782095807001/3092322318750000\) | \(1490160142248422400000000\) | \([2]\) | \(28311552\) | \(3.4050\) | |
| 223440.em4 | 223440cg4 | \([0, 1, 0, 31001304, -68083430220]\) | \(6837784281928633319/8113766016106800\) | \(-3909945172086574748467200\) | \([2]\) | \(28311552\) | \(3.4050\) |
Rank
sage: E.rank()
The elliptic curves in class 223440cg have rank \(0\).
Complex multiplication
The elliptic curves in class 223440cg do not have complex multiplication.Modular form 223440.2.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 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.
