Show commands:
SageMath
E = EllipticCurve("bw1")
E.isogeny_class()
Elliptic curves in class 149058bw
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
149058.hg2 | 149058bw1 | \([1, -1, 1, 53212153, -1688104631937]\) | \(40251338884511/2997011332224\) | \(-1240692815435975560139435136\) | \([]\) | \(75866112\) | \(3.8783\) | \(\Gamma_0(N)\)-optimal |
149058.hg1 | 149058bw2 | \([1, -1, 1, -273856513937, -55161007239852237]\) | \(-5486773802537974663600129/2635437714\) | \(-1091009767674920875345746\) | \([]\) | \(531062784\) | \(4.8513\) |
Rank
sage: E.rank()
The elliptic curves in class 149058bw have rank \(0\).
Complex multiplication
The elliptic curves in class 149058bw do not have complex multiplication.Modular form 149058.2.a.bw
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.
\(\left(\begin{array}{rr} 1 & 7 \\ 7 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.