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SageMath
E = EllipticCurve("t1")
E.isogeny_class()
Elliptic curves in class 230115t
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 230115.t2 | 230115t1 | \([0, 1, 1, -65607285, -182276857411]\) | \(210966209738334797824/25153051046653125\) | \(3723554272753675834003125\) | \([]\) | \(34214400\) | \(3.4457\) | \(\Gamma_0(N)\)-optimal |
| 230115.t1 | 230115t2 | \([0, 1, 1, -1258523445, 17158097831006]\) | \(1489157481162281146384384/2616603057861328125\) | \(387351159830620147705078125\) | \([]\) | \(102643200\) | \(3.9950\) |
Rank
sage: E.rank()
The elliptic curves in class 230115t have rank \(1\).
Complex multiplication
The elliptic curves in class 230115t do not have complex multiplication.Modular form 230115.2.a.t
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.
