Show commands:
SageMath
E = EllipticCurve("g1")
E.isogeny_class()
Elliptic curves in class 10626g
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 10626.h4 | 10626g1 | \([1, 0, 1, 36684, -11033630]\) | \(5459725204437026375/55780815891710448\) | \(-55780815891710448\) | \([6]\) | \(119808\) | \(1.8944\) | \(\Gamma_0(N)\)-optimal |
| 10626.h3 | 10626g2 | \([1, 0, 1, -575576, -156016798]\) | \(21087770069125509765625/1694619018457399188\) | \(1694619018457399188\) | \([6]\) | \(239616\) | \(2.2410\) | |
| 10626.h2 | 10626g3 | \([1, 0, 1, -2854611, -1857894866]\) | \(-2572552807198813678947625/2038409681283182592\) | \(-2038409681283182592\) | \([2]\) | \(359424\) | \(2.4438\) | |
| 10626.h1 | 10626g4 | \([1, 0, 1, -45682451, -118846422610]\) | \(10543186518294206197228515625/6611719873695552\) | \(6611719873695552\) | \([2]\) | \(718848\) | \(2.7903\) |
Rank
sage: E.rank()
The elliptic curves in class 10626g have rank \(0\).
Complex multiplication
The elliptic curves in class 10626g do not have complex multiplication.Modular form 10626.2.a.g
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
