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SageMath
E = EllipticCurve("gt1")
E.isogeny_class()
Elliptic curves in class 103488gt
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 103488.l1 | 103488gt1 | \([0, -1, 0, -3379497, 2417922081]\) | \(-35431687725461248/440311012911\) | \(-53045401966557428736\) | \([]\) | \(4976640\) | \(2.5953\) | \(\Gamma_0(N)\)-optimal |
| 103488.l2 | 103488gt2 | \([0, -1, 0, 11755623, 12346793649]\) | \(1491325446082364672/1410025768453071\) | \(-169869436551920998480896\) | \([]\) | \(14929920\) | \(3.1446\) |
Rank
sage: E.rank()
The elliptic curves in class 103488gt have rank \(0\).
Complex multiplication
The elliptic curves in class 103488gt do not have complex multiplication.Modular form 103488.2.a.gt
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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
