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SageMath
E = EllipticCurve("ib1")
E.isogeny_class()
Elliptic curves in class 482790ib
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 482790.ib3 | 482790ib1 | \([1, 0, 0, -1594480, 774713600]\) | \(253060782505556761/41184460800\) | \(72960784559308800\) | \([2]\) | \(8847360\) | \(2.2447\) | \(\Gamma_0(N)\)-optimal |
| 482790.ib2 | 482790ib2 | \([1, 0, 0, -1749360, 615094272]\) | \(334199035754662681/101099003040000\) | \(179103050924545440000\) | \([2, 2]\) | \(17694720\) | \(2.5913\) | |
| 482790.ib4 | 482790ib3 | \([1, 0, 0, 4784640, 4129079472]\) | \(6837784281928633319/8113766016106800\) | \(-14374031437260178714800\) | \([2]\) | \(35389440\) | \(2.9379\) | |
| 482790.ib1 | 482790ib4 | \([1, 0, 0, -10761440, -13113908400]\) | \(77799851782095807001/3092322318750000\) | \(5478237619327068750000\) | \([2]\) | \(35389440\) | \(2.9379\) |
Rank
sage: E.rank()
The elliptic curves in class 482790ib have rank \(1\).
Complex multiplication
The elliptic curves in class 482790ib do not have complex multiplication.Modular form 482790.2.a.ib
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.
