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SageMath
E = EllipticCurve("p1")
E.isogeny_class()
Elliptic curves in class 288834.p
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
288834.p1 | 288834p3 | \([1, 0, 1, -13783900, 19696450202]\) | \(-1956469094246217097/36641439744\) | \(-5424248106742972416\) | \([]\) | \(21170160\) | \(2.7192\) | |
288834.p2 | 288834p2 | \([1, 0, 1, -64285, 60070712]\) | \(-198461344537/10417365504\) | \(-1542143963422573056\) | \([]\) | \(7056720\) | \(2.1699\) | |
288834.p3 | 288834p1 | \([1, 0, 1, 7130, -2203168]\) | \(270840023/14329224\) | \(-2121239413520136\) | \([]\) | \(2352240\) | \(1.6206\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 288834.p have rank \(0\).
Complex multiplication
The elliptic curves in class 288834.p do not have complex multiplication.Modular form 288834.2.a.p
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.
\(\left(\begin{array}{rrr} 1 & 3 & 9 \\ 3 & 1 & 3 \\ 9 & 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.