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SageMath
E = EllipticCurve("ch1")
E.isogeny_class()
Elliptic curves in class 106560ch
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 106560.g3 | 106560ch1 | \([0, 0, 0, -20028, -1090928]\) | \(74385620944/1665\) | \(19886653440\) | \([2]\) | \(278528\) | \(1.0907\) | \(\Gamma_0(N)\)-optimal |
| 106560.g2 | 106560ch2 | \([0, 0, 0, -20748, -1008272]\) | \(20674973956/2772225\) | \(132445111910400\) | \([2, 2]\) | \(557056\) | \(1.4373\) | |
| 106560.g4 | 106560ch3 | \([0, 0, 0, 32532, -5334608]\) | \(39849102862/151723125\) | \(-14497370357760000\) | \([2]\) | \(1114112\) | \(1.7839\) | |
| 106560.g1 | 106560ch4 | \([0, 0, 0, -85548, 8608048]\) | \(724629215378/84337245\) | \(8058549253570560\) | \([2]\) | \(1114112\) | \(1.7839\) |
Rank
sage: E.rank()
The elliptic curves in class 106560ch have rank \(1\).
Complex multiplication
The elliptic curves in class 106560ch do not have complex multiplication.Modular form 106560.2.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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
