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SageMath
E = EllipticCurve("f1")
E.isogeny_class()
Elliptic curves in class 30960.f
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 30960.f1 | 30960bf4 | \([0, 0, 0, -746283, -214116262]\) | \(15393836938735081/2275690697640\) | \(6795176012101877760\) | \([2]\) | \(552960\) | \(2.3382\) | |
| 30960.f2 | 30960bf3 | \([0, 0, 0, -717483, -233913382]\) | \(13679527032530281/381633600\) | \(1139551823462400\) | \([2]\) | \(276480\) | \(1.9917\) | |
| 30960.f3 | 30960bf2 | \([0, 0, 0, -195483, 33231818]\) | \(276670733768281/336980250\) | \(1006217634816000\) | \([2]\) | \(184320\) | \(1.7889\) | |
| 30960.f4 | 30960bf1 | \([0, 0, 0, -15483, 219818]\) | \(137467988281/72562500\) | \(216670464000000\) | \([2]\) | \(92160\) | \(1.4423\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 30960.f have rank \(1\).
Complex multiplication
The elliptic curves in class 30960.f do not have complex multiplication.Modular form 30960.2.a.f
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.
