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SageMath
E = EllipticCurve("e1")
E.isogeny_class()
Elliptic curves in class 3825e
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
3825.i2 | 3825e1 | \([0, 0, 1, 150, 3406]\) | \(32768/459\) | \(-5228296875\) | \([]\) | \(1728\) | \(0.54550\) | \(\Gamma_0(N)\)-optimal |
3825.i1 | 3825e2 | \([0, 0, 1, -13350, 594031]\) | \(-23100424192/14739\) | \(-167886421875\) | \([]\) | \(5184\) | \(1.0948\) |
Rank
sage: E.rank()
The elliptic curves in class 3825e have rank \(0\).
Complex multiplication
The elliptic curves in class 3825e do not have complex multiplication.Modular form 3825.2.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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.