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SageMath
E = EllipticCurve("i1")
E.isogeny_class()
Elliptic curves in class 227430.i
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 227430.i1 | 227430fd3 | \([1, -1, 0, -288958005, 1824593621701]\) | \(77799851782095807001/3092322318750000\) | \(106055669281914738618750000\) | \([2]\) | \(70778880\) | \(3.7605\) | |
| 227430.i2 | 227430fd2 | \([1, -1, 0, -46972485, -85591676075]\) | \(334199035754662681/101099003040000\) | \(3467336624687850636960000\) | \([2, 2]\) | \(35389440\) | \(3.4139\) | |
| 227430.i3 | 227430fd1 | \([1, -1, 0, -42813765, -107800072619]\) | \(253060782505556761/41184460800\) | \(1412480687305708339200\) | \([2]\) | \(17694720\) | \(3.0673\) | \(\Gamma_0(N)\)-optimal |
| 227430.i4 | 227430fd4 | \([1, -1, 0, 128473515, -574489499675]\) | \(6837784281928633319/8113766016106800\) | \(-278273348162135750550193200\) | \([2]\) | \(70778880\) | \(3.7605\) |
Rank
sage: E.rank()
The elliptic curves in class 227430.i have rank \(1\).
Complex multiplication
The elliptic curves in class 227430.i do not have complex multiplication.Modular form 227430.2.a.i
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
