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SageMath
E = EllipticCurve("l1")
E.isogeny_class()
Elliptic curves in class 183872.l
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 183872.l1 | 183872h2 | \([0, 1, 0, -15097, 708423]\) | \(19248832/17\) | \(336100364288\) | \([2]\) | \(294912\) | \(1.1370\) | |
| 183872.l2 | 183872h1 | \([0, 1, 0, -732, 16030]\) | \(-140608/289\) | \(-89276659264\) | \([2]\) | \(147456\) | \(0.79045\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 183872.l have rank \(1\).
Complex multiplication
The elliptic curves in class 183872.l do not have complex multiplication.Modular form 183872.2.a.l
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.
