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SageMath
E = EllipticCurve("s1")
E.isogeny_class()
Elliptic curves in class 48300s
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 48300.v1 | 48300s1 | \([0, 1, 0, -252533, 48758688]\) | \(7124261256822784/475453125\) | \(118863281250000\) | \([2]\) | \(414720\) | \(1.7563\) | \(\Gamma_0(N)\)-optimal |
| 48300.v2 | 48300s2 | \([0, 1, 0, -236908, 55071188]\) | \(-367624742361424/115740505125\) | \(-462962020500000000\) | \([2]\) | \(829440\) | \(2.1029\) |
Rank
sage: E.rank()
The elliptic curves in class 48300s have rank \(0\).
Complex multiplication
The elliptic curves in class 48300s do not have complex multiplication.Modular form 48300.2.a.s
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.
