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SageMath
E = EllipticCurve("i1")
E.isogeny_class()
Elliptic curves in class 69360i
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
69360.a2 | 69360i1 | \([0, -1, 0, -11, -114]\) | \(-2048/75\) | \(-5895600\) | \([2]\) | \(15360\) | \(-0.020632\) | \(\Gamma_0(N)\)-optimal |
69360.a1 | 69360i2 | \([0, -1, 0, -436, -3344]\) | \(7304528/45\) | \(56597760\) | \([2]\) | \(30720\) | \(0.32594\) |
Rank
sage: E.rank()
The elliptic curves in class 69360i have rank \(1\).
Complex multiplication
The elliptic curves in class 69360i do not have complex multiplication.Modular form 69360.2.a.i
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.