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SageMath
E = EllipticCurve("e1")
E.isogeny_class()
Elliptic curves in class 7605e
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 7605.m2 | 7605e1 | \([0, 0, 1, 2028, -45588]\) | \(7077888/10985\) | \(-1431607415355\) | \([]\) | \(8064\) | \(1.0178\) | \(\Gamma_0(N)\)-optimal |
| 7605.m1 | 7605e2 | \([0, 0, 1, -63882, -6243325]\) | \(-303464448/1625\) | \(-154384882513875\) | \([]\) | \(24192\) | \(1.5671\) |
Rank
sage: E.rank()
The elliptic curves in class 7605e have rank \(0\).
Complex multiplication
The elliptic curves in class 7605e do not have complex multiplication.Modular form 7605.2.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.
