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SageMath
E = EllipticCurve("b1")
E.isogeny_class()
Elliptic curves in class 4368.b
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 4368.b1 | 4368d5 | \([0, -1, 0, -151424, 22730400]\) | \(187491149065688834/3549\) | \(7268352\) | \([4]\) | \(8192\) | \(1.3043\) | |
| 4368.b2 | 4368d3 | \([0, -1, 0, -9464, 357504]\) | \(91557481657828/12595401\) | \(12897690624\) | \([2, 4]\) | \(4096\) | \(0.95770\) | |
| 4368.b3 | 4368d6 | \([0, -1, 0, -8624, 422688]\) | \(-34639400027234/17130345141\) | \(-35082946848768\) | \([4]\) | \(8192\) | \(1.3043\) | |
| 4368.b4 | 4368d2 | \([0, -1, 0, -644, 4704]\) | \(115562131792/32867289\) | \(8414025984\) | \([2, 2]\) | \(2048\) | \(0.61113\) | |
| 4368.b5 | 4368d1 | \([0, -1, 0, -239, -1290]\) | \(94757435392/4179357\) | \(66869712\) | \([2]\) | \(1024\) | \(0.26455\) | \(\Gamma_0(N)\)-optimal |
| 4368.b6 | 4368d4 | \([0, -1, 0, 1696, 29040]\) | \(526556774012/674481717\) | \(-690669278208\) | \([2]\) | \(4096\) | \(0.95770\) |
Rank
sage: E.rank()
The elliptic curves in class 4368.b have rank \(0\).
Complex multiplication
The elliptic curves in class 4368.b do not have complex multiplication.Modular form 4368.2.a.b
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.
\(\left(\begin{array}{rrrrrr} 1 & 2 & 4 & 4 & 8 & 8 \\ 2 & 1 & 2 & 2 & 4 & 4 \\ 4 & 2 & 1 & 4 & 8 & 8 \\ 4 & 2 & 4 & 1 & 2 & 2 \\ 8 & 4 & 8 & 2 & 1 & 4 \\ 8 & 4 & 8 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
