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SageMath
E = EllipticCurve("e1")
E.isogeny_class()
Elliptic curves in class 352800.e
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
352800.e1 | 352800e2 | \([0, 0, 0, -10598700, -13243916000]\) | \(69934528/225\) | \(423616024843200000000\) | \([2]\) | \(22020096\) | \(2.8241\) | |
352800.e2 | 352800e1 | \([0, 0, 0, -951825, -8403500]\) | \(3241792/1875\) | \(55158336568125000000\) | \([2]\) | \(11010048\) | \(2.4775\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 352800.e have rank \(2\).
Complex multiplication
The elliptic curves in class 352800.e do not have complex multiplication.Modular form 352800.2.a.e
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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.