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SageMath
E = EllipticCurve("m1")
E.isogeny_class()
Elliptic curves in class 1350.m
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 1350.m1 | 1350p2 | \([1, -1, 1, -455, 3647]\) | \(68450475/4096\) | \(622080000\) | \([3]\) | \(864\) | \(0.44013\) | |
| 1350.m2 | 1350p1 | \([1, -1, 1, -80, -253]\) | \(3316275/16\) | \(270000\) | \([]\) | \(288\) | \(-0.10918\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 1350.m have rank \(1\).
Complex multiplication
The elliptic curves in class 1350.m do not have complex multiplication.Modular form 1350.2.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 LMFDB 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 LMFDB labels.
