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SageMath
E = EllipticCurve("t1")
E.isogeny_class()
Elliptic curves in class 76050.t
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 76050.t1 | 76050dd2 | \([1, -1, 0, -85617, 20879041]\) | \(-110940205/236196\) | \(-147771321932812500\) | \([]\) | \(1152000\) | \(1.9835\) | |
| 76050.t2 | 76050dd1 | \([1, -1, 0, -3717, -169259]\) | \(-5674525/9216\) | \(-9225290880000\) | \([]\) | \(230400\) | \(1.1788\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 76050.t have rank \(0\).
Complex multiplication
The elliptic curves in class 76050.t do not have complex multiplication.Modular form 76050.2.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 LMFDB numbering.
\(\left(\begin{array}{rr} 1 & 5 \\ 5 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
