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SageMath
E = EllipticCurve("f1")
E.isogeny_class()
Elliptic curves in class 3675.f
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 3675.f1 | 3675l3 | \([1, 0, 0, -137838, 19684167]\) | \(157551496201/13125\) | \(24127236328125\) | \([2]\) | \(18432\) | \(1.6117\) | |
| 3675.f2 | 3675l2 | \([1, 0, 0, -9213, 261792]\) | \(47045881/11025\) | \(20266878515625\) | \([2, 2]\) | \(9216\) | \(1.2651\) | |
| 3675.f3 | 3675l1 | \([1, 0, 0, -3088, -62833]\) | \(1771561/105\) | \(193017890625\) | \([2]\) | \(4608\) | \(0.91856\) | \(\Gamma_0(N)\)-optimal |
| 3675.f4 | 3675l4 | \([1, 0, 0, 21412, 1639917]\) | \(590589719/972405\) | \(-1787538685078125\) | \([2]\) | \(18432\) | \(1.6117\) |
Rank
sage: E.rank()
The elliptic curves in class 3675.f have rank \(1\).
Complex multiplication
The elliptic curves in class 3675.f do not have complex multiplication.Modular form 3675.2.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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
