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SageMath
E = EllipticCurve("ev1")
E.isogeny_class()
Elliptic curves in class 149058ev
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 149058.v4 | 149058ev1 | \([1, -1, 0, -1454868, 14101678800]\) | \(-822656953/207028224\) | \(-85704857818693065179136\) | \([2]\) | \(15482880\) | \(3.0797\) | \(\Gamma_0(N)\)-optimal |
| 149058.v3 | 149058ev2 | \([1, -1, 0, -96851988, 363541329360]\) | \(242702053576633/2554695936\) | \(1057584554098638253519104\) | \([2, 2]\) | \(30965760\) | \(3.4262\) | |
| 149058.v1 | 149058ev3 | \([1, -1, 0, -1545695748, 23390594744544]\) | \(986551739719628473/111045168\) | \(45970110504801919970352\) | \([2]\) | \(61931520\) | \(3.7728\) | |
| 149058.v2 | 149058ev4 | \([1, -1, 0, -174362148, -300519215424]\) | \(1416134368422073/725251155408\) | \(300237068918127356884853712\) | \([2]\) | \(61931520\) | \(3.7728\) |
Rank
sage: E.rank()
The elliptic curves in class 149058ev have rank \(1\).
Complex multiplication
The elliptic curves in class 149058ev do not have complex multiplication.Modular form 149058.2.a.ev
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.
