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SageMath
E = EllipticCurve("i1")
E.isogeny_class()
Elliptic curves in class 720i
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 720.h3 | 720i1 | \([0, 0, 0, -12, 11]\) | \(16384/5\) | \(58320\) | \([2]\) | \(48\) | \(-0.38064\) | \(\Gamma_0(N)\)-optimal |
| 720.h4 | 720i2 | \([0, 0, 0, 33, 74]\) | \(21296/25\) | \(-4665600\) | \([2]\) | \(96\) | \(-0.034070\) | |
| 720.h1 | 720i3 | \([0, 0, 0, -372, -2761]\) | \(488095744/125\) | \(1458000\) | \([2]\) | \(144\) | \(0.16866\) | |
| 720.h2 | 720i4 | \([0, 0, 0, -327, -3454]\) | \(-20720464/15625\) | \(-2916000000\) | \([2]\) | \(288\) | \(0.51524\) |
Rank
sage: E.rank()
The elliptic curves in class 720i have rank \(0\).
Complex multiplication
The elliptic curves in class 720i do not have complex multiplication.Modular form 720.2.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.
\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
