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SageMath
sage: E = EllipticCurve("n1")
sage: E.isogeny_class()
Elliptic curves in class 15680.n
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 15680.n1 | 15680s3 | \([0, 1, 0, -8101, 277899]\) | \(488095744/125\) | \(15059072000\) | \([2]\) | \(17280\) | \(0.93888\) | |
| 15680.n2 | 15680s4 | \([0, 1, 0, -7121, 348655]\) | \(-20720464/15625\) | \(-30118144000000\) | \([2]\) | \(34560\) | \(1.2855\) | |
| 15680.n3 | 15680s1 | \([0, 1, 0, -261, -1205]\) | \(16384/5\) | \(602362880\) | \([2]\) | \(5760\) | \(0.38958\) | \(\Gamma_0(N)\)-optimal |
| 15680.n4 | 15680s2 | \([0, 1, 0, 719, -7281]\) | \(21296/25\) | \(-48189030400\) | \([2]\) | \(11520\) | \(0.73615\) |
Rank
sage: E.rank()
The elliptic curves in class 15680.n have rank \(0\).
Complex multiplication
The elliptic curves in class 15680.n do not have complex multiplication.Modular form 15680.2.a.n
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
