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SageMath
E = EllipticCurve("i1")
E.isogeny_class()
Elliptic curves in class 29400.i
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 29400.i1 | 29400r6 | \([0, -1, 0, -12838408, 17709656812]\) | \(62161150998242/1607445\) | \(6051657497760000000\) | \([2]\) | \(1179648\) | \(2.7106\) | |
| 29400.i2 | 29400r4 | \([0, -1, 0, -833408, 254386812]\) | \(34008619684/4862025\) | \(9152198067600000000\) | \([2, 2]\) | \(589824\) | \(2.3640\) | |
| 29400.i3 | 29400r2 | \([0, -1, 0, -220908, -35938188]\) | \(2533446736/275625\) | \(129708022500000000\) | \([2, 2]\) | \(294912\) | \(2.0174\) | |
| 29400.i4 | 29400r1 | \([0, -1, 0, -214783, -38241188]\) | \(37256083456/525\) | \(15441431250000\) | \([2]\) | \(147456\) | \(1.6709\) | \(\Gamma_0(N)\)-optimal |
| 29400.i5 | 29400r3 | \([0, -1, 0, 293592, -178969188]\) | \(1486779836/8203125\) | \(-15441431250000000000\) | \([2]\) | \(589824\) | \(2.3640\) | |
| 29400.i6 | 29400r5 | \([0, -1, 0, 1371592, 1370116812]\) | \(75798394558/259416045\) | \(-976641224902560000000\) | \([2]\) | \(1179648\) | \(2.7106\) |
Rank
sage: E.rank()
The elliptic curves in class 29400.i have rank \(0\).
Complex multiplication
The elliptic curves in class 29400.i do not have complex multiplication.Modular form 29400.2.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.
\(\left(\begin{array}{rrrrrr} 1 & 2 & 4 & 8 & 8 & 4 \\ 2 & 1 & 2 & 4 & 4 & 2 \\ 4 & 2 & 1 & 2 & 2 & 4 \\ 8 & 4 & 2 & 1 & 4 & 8 \\ 8 & 4 & 2 & 4 & 1 & 8 \\ 4 & 2 & 4 & 8 & 8 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
