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SageMath
E = EllipticCurve("g1")
E.isogeny_class()
Elliptic curves in class 50715g
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 50715.r1 | 50715g1 | \([1, -1, 1, -1829792, -928136366]\) | \(292583028222603/8456021875\) | \(19581485273367215625\) | \([2]\) | \(1244160\) | \(2.4797\) | \(\Gamma_0(N)\)-optimal |
| 50715.r2 | 50715g2 | \([1, -1, 1, 439153, -3080003804]\) | \(4044759171237/1771943359375\) | \(-4103263131263173828125\) | \([2]\) | \(2488320\) | \(2.8263\) |
Rank
sage: E.rank()
The elliptic curves in class 50715g have rank \(0\).
Complex multiplication
The elliptic curves in class 50715g do not have complex multiplication.Modular form 50715.2.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.
