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SageMath
E = EllipticCurve("o1")
E.isogeny_class()
Elliptic curves in class 15030o
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
15030.m2 | 15030o1 | \([1, -1, 1, 6448, -1826449]\) | \(40675641638471/1996889557500\) | \(-1455732487417500\) | \([2]\) | \(86016\) | \(1.5893\) | \(\Gamma_0(N)\)-optimal |
15030.m1 | 15030o2 | \([1, -1, 1, -190382, -30642361]\) | \(1046819248735488409/47650971093750\) | \(34737557927343750\) | \([2]\) | \(172032\) | \(1.9358\) |
Rank
sage: E.rank()
The elliptic curves in class 15030o have rank \(0\).
Complex multiplication
The elliptic curves in class 15030o do not have complex multiplication.Modular form 15030.2.a.o
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.