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SageMath
E = EllipticCurve("da1")
E.isogeny_class()
Elliptic curves in class 149058.da
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 149058.da1 | 149058gf3 | \([1, -1, 0, -145817541, 677639137657]\) | \(828279937799497/193444524\) | \(80081522726219002369836\) | \([2]\) | \(24772608\) | \(3.3854\) | |
| 149058.da2 | 149058gf2 | \([1, -1, 0, -10174761, 7970732797]\) | \(281397674377/96589584\) | \(39985835764531847548176\) | \([2, 2]\) | \(12386304\) | \(3.0388\) | |
| 149058.da3 | 149058gf1 | \([1, -1, 0, -4212441, -3234851411]\) | \(19968681097/628992\) | \(260388022886654277888\) | \([2]\) | \(6193152\) | \(2.6922\) | \(\Gamma_0(N)\)-optimal |
| 149058.da4 | 149058gf4 | \([1, -1, 0, 30070899, 55388169409]\) | \(7264187703863/7406095788\) | \(-3065950981167483606911532\) | \([2]\) | \(24772608\) | \(3.3854\) |
Rank
sage: E.rank()
The elliptic curves in class 149058.da have rank \(1\).
Complex multiplication
The elliptic curves in class 149058.da do not have complex multiplication.Modular form 149058.2.a.da
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.
