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SageMath
E = EllipticCurve("m1")
E.isogeny_class()
Elliptic curves in class 3150m
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
3150.a2 | 3150m1 | \([1, -1, 0, 5508, 11416]\) | \(2595575/1512\) | \(-10764140625000\) | \([]\) | \(8640\) | \(1.1900\) | \(\Gamma_0(N)\)-optimal |
3150.a1 | 3150m2 | \([1, -1, 0, -78867, 9039541]\) | \(-7620530425/526848\) | \(-3750705000000000\) | \([]\) | \(25920\) | \(1.7393\) |
Rank
sage: E.rank()
The elliptic curves in class 3150m have rank \(0\).
Complex multiplication
The elliptic curves in class 3150m do not have complex multiplication.Modular form 3150.2.a.m
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.