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SageMath
E = EllipticCurve("m1")
E.isogeny_class()
Elliptic curves in class 463680m
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 463680.m3 | 463680m1 | \([0, 0, 0, -18408, 429928]\) | \(924093773824/427810005\) | \(319358457492480\) | \([2]\) | \(1376256\) | \(1.4777\) | \(\Gamma_0(N)\)-optimal |
| 463680.m2 | 463680m2 | \([0, 0, 0, -149628, -21982448]\) | \(31018076123344/472410225\) | \(5642437493145600\) | \([2, 2]\) | \(2752512\) | \(1.8243\) | |
| 463680.m4 | 463680m3 | \([0, 0, 0, -13548, -60465872]\) | \(-5756278756/33056218125\) | \(-1579285414748160000\) | \([2]\) | \(5505024\) | \(2.1709\) | |
| 463680.m1 | 463680m4 | \([0, 0, 0, -2385228, -1417891088]\) | \(31412749404762436/7455105\) | \(356173187973120\) | \([2]\) | \(5505024\) | \(2.1709\) |
Rank
sage: E.rank()
The elliptic curves in class 463680m have rank \(1\).
Complex multiplication
The elliptic curves in class 463680m do not have complex multiplication.Modular form 463680.2.a.m
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.
