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SageMath
E = EllipticCurve("ch1")
E.isogeny_class()
Elliptic curves in class 149058ch
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
149058.ib2 | 149058ch1 | \([1, -1, 1, 222034, -25464981]\) | \(17303/14\) | \(-979468836089845374\) | \([]\) | \(2695680\) | \(2.1400\) | \(\Gamma_0(N)\)-optimal |
149058.ib1 | 149058ch2 | \([1, -1, 1, -4622351, -3881595441]\) | \(-156116857/2744\) | \(-191975891873609693304\) | \([]\) | \(8087040\) | \(2.6893\) |
Rank
sage: E.rank()
The elliptic curves in class 149058ch have rank \(0\).
Complex multiplication
The elliptic curves in class 149058ch do not have complex multiplication.Modular form 149058.2.a.ch
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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.