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SageMath
E = EllipticCurve("i1")
E.isogeny_class()
Elliptic curves in class 152944.i
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 152944.i1 | 152944g3 | \([0, -1, 0, -10099184, -12349765184]\) | \(15698803397448457/20709376\) | \(150273732017913856\) | \([]\) | \(4147200\) | \(2.5720\) | |
| 152944.i2 | 152944g2 | \([0, -1, 0, -157824, -7184384]\) | \(59914169497/31554496\) | \(228969326543896576\) | \([]\) | \(1382400\) | \(2.0226\) | |
| 152944.i3 | 152944g1 | \([0, -1, 0, -90064, 10433216]\) | \(11134383337/316\) | \(2292995178496\) | \([]\) | \(460800\) | \(1.4733\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 152944.i have rank \(0\).
Complex multiplication
The elliptic curves in class 152944.i do not have complex multiplication.Modular form 152944.2.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 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.
