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SageMath
E = EllipticCurve("i1")
E.isogeny_class()
Elliptic curves in class 17472i
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
17472.c3 | 17472i1 | \([0, -1, 0, 863, 92449]\) | \(270840023/14329224\) | \(-3756320096256\) | \([]\) | \(41472\) | \(1.0926\) | \(\Gamma_0(N)\)-optimal |
17472.c2 | 17472i2 | \([0, -1, 0, -7777, -2525471]\) | \(-198461344537/10417365504\) | \(-2730849862680576\) | \([]\) | \(124416\) | \(1.6419\) | |
17472.c1 | 17472i3 | \([0, -1, 0, -1667617, -828339551]\) | \(-1956469094246217097/36641439744\) | \(-9605333580251136\) | \([]\) | \(373248\) | \(2.1912\) |
Rank
sage: E.rank()
The elliptic curves in class 17472i have rank \(0\).
Complex multiplication
The elliptic curves in class 17472i do not have complex multiplication.Modular form 17472.2.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.
\(\left(\begin{array}{rrr} 1 & 3 & 9 \\ 3 & 1 & 3 \\ 9 & 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.