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SageMath
E = EllipticCurve("i1")
E.isogeny_class()
Elliptic curves in class 303600i
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
303600.i3 | 303600i1 | \([0, -1, 0, -15383, -719238]\) | \(1610404796416/25255725\) | \(6313931250000\) | \([2]\) | \(786432\) | \(1.2569\) | \(\Gamma_0(N)\)-optimal |
303600.i2 | 303600i2 | \([0, -1, 0, -30508, 944512]\) | \(785089500496/360050625\) | \(1440202500000000\) | \([2, 2]\) | \(1572864\) | \(1.6035\) | |
303600.i1 | 303600i3 | \([0, -1, 0, -410008, 101132512]\) | \(476411000270404/296484375\) | \(4743750000000000\) | \([2]\) | \(3145728\) | \(1.9501\) | |
303600.i4 | 303600i4 | \([0, -1, 0, 106992, 6994512]\) | \(8465518982876/6233458275\) | \(-99735332400000000\) | \([2]\) | \(3145728\) | \(1.9501\) |
Rank
sage: E.rank()
The elliptic curves in class 303600i have rank \(1\).
Complex multiplication
The elliptic curves in class 303600i do not have complex multiplication.Modular form 303600.2.a.i
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.