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SageMath
E = EllipticCurve("e1")
E.isogeny_class()
Elliptic curves in class 243360e
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
243360.e2 | 243360e1 | \([0, 0, 0, -4953, -116948]\) | \(131096512/18225\) | \(1868121403200\) | \([2]\) | \(516096\) | \(1.0811\) | \(\Gamma_0(N)\)-optimal |
243360.e1 | 243360e2 | \([0, 0, 0, -20748, 1032928]\) | \(150568768/16875\) | \(110703490560000\) | \([2]\) | \(1032192\) | \(1.4277\) |
Rank
sage: E.rank()
The elliptic curves in class 243360e have rank \(2\).
Complex multiplication
The elliptic curves in class 243360e do not have complex multiplication.Modular form 243360.2.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 Cremona 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 Cremona labels.