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SageMath
E = EllipticCurve("a1")
E.isogeny_class()
Elliptic curves in class 150a
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 150.c4 | 150a1 | \([1, 0, 0, -3, -3]\) | \(-24389/12\) | \(-1500\) | \([2]\) | \(8\) | \(-0.68527\) | \(\Gamma_0(N)\)-optimal |
| 150.c2 | 150a2 | \([1, 0, 0, -53, -153]\) | \(131872229/18\) | \(2250\) | \([2]\) | \(16\) | \(-0.33870\) | |
| 150.c3 | 150a3 | \([1, 0, 0, -28, 272]\) | \(-19465109/248832\) | \(-31104000\) | \([10]\) | \(40\) | \(0.11945\) | |
| 150.c1 | 150a4 | \([1, 0, 0, -828, 9072]\) | \(502270291349/1889568\) | \(236196000\) | \([10]\) | \(80\) | \(0.46602\) |
Rank
sage: E.rank()
The elliptic curves in class 150a have rank \(0\).
Complex multiplication
The elliptic curves in class 150a do not have complex multiplication.Modular form 150.2.a.a
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 5 & 10 \\ 2 & 1 & 10 & 5 \\ 5 & 10 & 1 & 2 \\ 10 & 5 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
