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SageMath
E = EllipticCurve("g1")
E.isogeny_class()
Elliptic curves in class 43758.g
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 43758.g1 | 43758e2 | \([1, -1, 0, -18612, -972556]\) | \(26409015101734875/3994998436\) | \(107864957772\) | \([2]\) | \(77824\) | \(1.1298\) | |
| 43758.g2 | 43758e1 | \([1, -1, 0, -1272, -11920]\) | \(8433606238875/2484248624\) | \(67074712848\) | \([2]\) | \(38912\) | \(0.78321\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 43758.g have rank \(1\).
Complex multiplication
The elliptic curves in class 43758.g do not have complex multiplication.Modular form 43758.2.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 LMFDB 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 LMFDB labels.
