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SageMath
E = EllipticCurve("l1")
E.isogeny_class()
Elliptic curves in class 84150l
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 84150.z1 | 84150l1 | \([1, -1, 0, -9042, -277884]\) | \(193802978403/31790000\) | \(13411406250000\) | \([2]\) | \(294912\) | \(1.2406\) | \(\Gamma_0(N)\)-optimal |
| 84150.z2 | 84150l2 | \([1, -1, 0, 16458, -1578384]\) | \(1168574089437/3214062500\) | \(-1355932617187500\) | \([2]\) | \(589824\) | \(1.5872\) |
Rank
sage: E.rank()
The elliptic curves in class 84150l have rank \(0\).
Complex multiplication
The elliptic curves in class 84150l do not have complex multiplication.Modular form 84150.2.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 Cremona 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 Cremona labels.
