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SageMath
E = EllipticCurve("t1")
E.isogeny_class()
Elliptic curves in class 1152.t
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 1152.t1 | 1152i1 | \([0, 0, 0, -318, 2180]\) | \(19056256/27\) | \(5038848\) | \([2]\) | \(384\) | \(0.18920\) | \(\Gamma_0(N)\)-optimal |
| 1152.t2 | 1152i2 | \([0, 0, 0, -228, 3440]\) | \(-219488/729\) | \(-4353564672\) | \([2]\) | \(768\) | \(0.53578\) |
Rank
sage: E.rank()
The elliptic curves in class 1152.t have rank \(0\).
Complex multiplication
The elliptic curves in class 1152.t do not have complex multiplication.Modular form 1152.2.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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
