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SageMath
E = EllipticCurve("r1")
E.isogeny_class()
Elliptic curves in class 149058.r
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
149058.r1 | 149058he2 | \([1, -1, 0, -6945171, -7043846419]\) | \(-67645179/8\) | \(-4381529231265817176\) | \([]\) | \(6967296\) | \(2.6025\) | |
149058.r2 | 149058he1 | \([1, -1, 0, 10869, -29839419]\) | \(189/512\) | \(-384661002470524416\) | \([]\) | \(2322432\) | \(2.0532\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 149058.r have rank \(1\).
Complex multiplication
The elliptic curves in class 149058.r do not have complex multiplication.Modular form 149058.2.a.r
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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.