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SageMath
E = EllipticCurve("l1")
E.isogeny_class()
Elliptic curves in class 53520.l
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 53520.l1 | 53520q2 | \([0, -1, 0, -3620000, 3851986560]\) | \(-1280824409818832580001/822726139895701410\) | \(-3369886269012792975360\) | \([]\) | \(3358656\) | \(2.8320\) | |
| 53520.l2 | 53520q1 | \([0, -1, 0, -108800, -15360000]\) | \(-34773983355859201/4877010000000\) | \(-19976232960000000\) | \([]\) | \(479808\) | \(1.8591\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 53520.l have rank \(0\).
Complex multiplication
The elliptic curves in class 53520.l do not have complex multiplication.Modular form 53520.2.a.l
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.
\(\left(\begin{array}{rr} 1 & 7 \\ 7 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
