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SageMath
E = EllipticCurve("l1")
E.isogeny_class()
Elliptic curves in class 14800l
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
14800.ba3 | 14800l1 | \([0, 1, 0, -1333, -19037]\) | \(4096000/37\) | \(2368000000\) | \([]\) | \(6912\) | \(0.62134\) | \(\Gamma_0(N)\)-optimal |
14800.ba2 | 14800l2 | \([0, 1, 0, -9333, 332963]\) | \(1404928000/50653\) | \(3241792000000\) | \([]\) | \(20736\) | \(1.1706\) | |
14800.ba1 | 14800l3 | \([0, 1, 0, -749333, 249416963]\) | \(727057727488000/37\) | \(2368000000\) | \([]\) | \(62208\) | \(1.7199\) |
Rank
sage: E.rank()
The elliptic curves in class 14800l have rank \(0\).
Complex multiplication
The elliptic curves in class 14800l do not have complex multiplication.Modular form 14800.2.a.l
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.