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SageMath
E = EllipticCurve("m1")
E.isogeny_class()
Elliptic curves in class 3696m
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
3696.b1 | 3696m1 | \([0, -1, 0, -17242, -875009]\) | \(-35431687725461248/440311012911\) | \(-7044976206576\) | \([]\) | \(12960\) | \(1.2758\) | \(\Gamma_0(N)\)-optimal |
3696.b2 | 3696m2 | \([0, -1, 0, 59978, -4520981]\) | \(1491325446082364672/1410025768453071\) | \(-22560412295249136\) | \([]\) | \(38880\) | \(1.8251\) |
Rank
sage: E.rank()
The elliptic curves in class 3696m have rank \(0\).
Complex multiplication
The elliptic curves in class 3696m do not have complex multiplication.Modular form 3696.2.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.