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SageMath
E = EllipticCurve("l1")
E.isogeny_class()
Elliptic curves in class 2450.l
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 2450.l1 | 2450e4 | \([1, -1, 0, -327917, 72354491]\) | \(2121328796049/120050\) | \(220683788281250\) | \([2]\) | \(18432\) | \(1.8167\) | |
| 2450.l2 | 2450e3 | \([1, -1, 0, -107417, -12636009]\) | \(74565301329/5468750\) | \(10053015136718750\) | \([2]\) | \(18432\) | \(1.8167\) | |
| 2450.l3 | 2450e2 | \([1, -1, 0, -21667, 998241]\) | \(611960049/122500\) | \(225187539062500\) | \([2, 2]\) | \(9216\) | \(1.4701\) | |
| 2450.l4 | 2450e1 | \([1, -1, 0, 2833, 91741]\) | \(1367631/2800\) | \(-5147143750000\) | \([2]\) | \(4608\) | \(1.1235\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 2450.l have rank \(0\).
Complex multiplication
The elliptic curves in class 2450.l do not have complex multiplication.Modular form 2450.2.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.
\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
