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SageMath
E = EllipticCurve("g1")
E.isogeny_class()
Elliptic curves in class 110946g
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 110946.h1 | 110946g1 | \([1, 1, 0, -17197505, -27431190411]\) | \(118417788018699625/130877227008\) | \(621680471061020540928\) | \([2]\) | \(5806080\) | \(2.9046\) | \(\Gamma_0(N)\)-optimal |
| 110946.h2 | 110946g2 | \([1, 1, 0, -12894145, -41488546187]\) | \(-49911230110731625/127619866649088\) | \(-606207669805687367582208\) | \([2]\) | \(11612160\) | \(3.2512\) |
Rank
sage: E.rank()
The elliptic curves in class 110946g have rank \(0\).
Complex multiplication
The elliptic curves in class 110946g do not have complex multiplication.Modular form 110946.2.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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
