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SageMath
E = EllipticCurve("l1")
E.isogeny_class()
Elliptic curves in class 192027.l
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 192027.l1 | 192027p2 | \([1, 1, 0, -79244475, -269440692066]\) | \(209849322390625/1882056627\) | \(493578022105897866385083\) | \([2]\) | \(20275200\) | \(3.3692\) | |
| 192027.l2 | 192027p1 | \([1, 1, 0, -1473540, -10012407093]\) | \(-1349232625/164333367\) | \(-43097182670403586608543\) | \([2]\) | \(10137600\) | \(3.0226\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 192027.l have rank \(1\).
Complex multiplication
The elliptic curves in class 192027.l do not have complex multiplication.Modular form 192027.2.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.
